Melisha Boyd Thompson will deliver her initial sermon 5 p.m. Sunday at Word of Truth Christian Fellowship, 1401 N. Carolina St. The Instruments of Praise will provide music.
St. Mark Church of Christ, Faro, will celebrate its 100th anniversary 11 a.m. and 3 p.m. Sunday. Co-pastor Alva Carlisle McGowan from Shining Light Bible Mission, Columbus, Ohio, will preach during the morning service. General bishop Alton Smith from St. Mark Church of Christ, Goldsboro, will preach during the afternoon service.
The Earlena Hinson Concert Series at First Baptist Church of Goldsboro will present the sanctuary choir and chamber ensemble in "A Festival of Hymns," arranged by Hal H. Hopson, 4 p.m. Sunday in the sanctuary. Admission is free; donations will be accepted. For more information, call Carl Ashley at 919-735-2516.
Union Grove Missionary Baptist Church, Fremont, will observe quarterly meeting service 11 a.m. March 17. Pastor James Lucas will deliver the message. Dinner will be served after the service. A commemoration of the death, burial and resurrection of Jesus will be observed 3 p.m. March 17. Pastor Fred Presely and First Baptist Church of Eureka will render the service. Union Grove will observe Fellowship Day 11 a.m. March 31. Pastor Robert Richardson and First Baptist Church of Murfreesboro will render the service. Dinner will be served.
The Rev. Claudia M. Frost will speak on "Unplugged" during service 11 a.m. Sunday at Outlaw's Bridge Universalist Church, 4408 N.C. 111 N., Seven Springs.
New Stoney Hill United Holy Church, 1003 Poplar St., will have prayer 9 a.m. Saturday. Sunday school will be 9:30 a.m. and worship 11 a.m. Sunday. Dr. Howard E. McNair will preach. The senior choir will sing, followed by Holy Communion. Bible study will be 7 p.m. Wednesday.
Atkinson Chapel Missionary Baptist Church, 634 S. Oak Forest Road, will observe Family and Friends Day with Sunday school 9:30 a.m. and worship 11 a.m. Sunday. The Rev. Tracy Lewis will preach. The choir will sing. A fellowship dinner will be served after the service.
Elm Grove Church Ministries' PWOP ministry will sponsor service 7:30 p.m. today. The speaker will be evangelist Wanda Guilford. A dinner plate sale will be 10 a.m. to 2 p.m. Saturday in the Family Dollar parking lot at 553 W. New Hope Road. To place orders or for delivery, call 919-344-1057. Sunday school will be 9 a.m. and worship 10 a.m. Sunday. Study of the word will be 11 a.m. and 7:30 p.m. Wednesday. PWOP ministry will be on assignment 1:30 p.m. Wednesday at Brian Center.
St. Luke United Methodist Church, 1608 E. Pine St., will have contemporary service 8:30 a.m. and worship 11 a.m. Sunday. Celebrate Recovery will be 6 p.m. Monday. St. Luke UMC is hosting community Lent services at noon on Wednesdays.
Salem United Methodist Church, 2706 Salem Church Road, will not have Sunday school. Worship with pastor Liz Hounshell will be 11 a.m. Sunday. A nursery and children's church will be provided. A family and friends covered-dish lunch will be served at noon Sunday. For more information, call 919-735-9210 or visit www.salemumcgoldsboro.com.
Holly Hill Church, 644 N. Beston Road, will have Sunday school 9:30 a.m. and worship 11 a.m. Sunday. Elder B.K. Robinson will preach. God's Chosen will provide music. Holly Hill Church will celebrate the deacons, mothers and trustees' anniversary 3 p.m. Sunday. Guests will be elder Tyrone Haney and St. Peter Church of Kinston. Bible study will be 7:15 p.m. Tuesday.
Pathway to Life United Holy Church, 600 Sycamore St., Fremont, will have Sunday school 9:30 a.m. and a Pastoral Day service with pastor Helen Reid 10:30 a.m. Sunday. Pastor Brent Murphy of New Birth Bible Fellowship, Raleigh, will render a pre-anniversary service 3 p.m. Sunday. Bible study will be 7:30 p.m. Tuesday.
Fremont Holiness Church, 726 Norwayne School Road, Fremont, will have spring revival 7:30 p.m. March 25-27. The speaker will be the Rev. Johnny Chavis.
The men's ministry kickoff at Adamsville Baptist Church, 1302 N. Berkeley Blvd., will be 7 a.m. Saturday. All men are welcome to attend and find out about opportunities to serve. Sunday school will be 9:15 a.m. and worship 10:30 a.m. and 6:30 p.m. Sunday. Pastor Ryne Fullerton will deliver the message. AWANA and adult Bible study and prayer meeting will be 6:30 p.m. Wednesday. During March, Adamsville Baptist Church is collecting craft items for Operation Christmas Child. For more information, visit www.adamsville.org or call the church office 919-778-1213.
Antioch Missionary Baptist Church, 601 W. Elm St., will have worship 10 a.m. Sunday. Bible study will be noon and 6 p.m. Wednesday. Pastor Tate will preach and the Antioch Missionary Baptist Church choir will sing 3 p.m. March 17 at Bible Faith Missionary Baptist Church.
The leadership planning meeting for the North Carolina Annual Conference will be 10 a.m. Saturday at New St. John AME Church, 1307 S. Slocumb St. The Annual Conference choir will rehearse at the church at noon Saturday. New St. John AME Church will have church school 10 a.m. and worship 11 a.m. Sunday. The Rev. James N. Sheares will bring the message. The praise team will provide music. Bible study will be 6 p.m. Wednesday.
Revelation Mission Free Will Baptist Church, 105 S. Bright St., will have quarterly meeting beginning with Holy Communion 7 p.m. Saturday. Pastor William A. Mitchell Jr. will deliver the message. The Greater St. John Free Will Baptist Church choir will sing. Dr. Juanita Whitfield will deliver the message 11 a.m. Sunday.
St. James AME Zion Church, 205 S. George St., will have a leaders meeting 10 a.m. Saturday. Services on Sunday will begin at 8 a.m. and 11 a.m. The Rev. Ronald Miller will preach. Sunday school will begin at 9:45 a.m. Senior Bible study will be at noon Tuesday. Bible study will be 6 p.m. Tuesday.
Shady Grove Missionary Baptist Church, 2506 New Hope Road, LaGrange, will have Sunday school 9:30 a.m. and worship 11 a.m. Sunday. Dr. Wilbert B. Johnson will deliver the message. The adult choir will sing. Bible study will be 6:30 p.m. Wednesday.
Deliverance Temple of God will have a pastoral service 11 a.m. Sunday with apostle Ronnie Harris. Apostle Teresa White will preach 4 p.m. Sunday.
Faith Presbyterian Church, 2114 N. Berkeley Blvd., will have a breakfast buffet meeting 9:30 a.m. Saturday at Artis Daily Bread, 2103 N. William St. Sunday school will be 10 a.m. and a Women's Day celebration 11 a.m. Sunday. The guest speaker will be Madie D. Bell. Bible study will be 6:30 p.m. Tuesday.
Holy Ghost Cathedral will have Sunday school 10:15 a.m., praise and worship at 11:15 a.m. and a message by apostle Preston Grimes 11:30 a.m. Sunday. The praise team will provide music.
Fertile Ground Ministry, 509 N. Carolina St., will have a "Helping a Sister Out" movie outing at 11 Saturday. "Going Up in Power Hour" will be 9:15 a.m. Sunday. Worship will be 10:30 a.m. Sunday. Pastor Willie Faison will preach. Fertile Ground Ministry will have a Founders Day service 2:30 p.m. Sunday. Guests will include Danny Uzzell and Wave of Glory. Prayer and Bible study will be 6:30 p.m. Wednesday. For more information, call 919-252-4342.
Little Rock Church, 1307 N.C. 581 N., is seeking a dependable musician for second and fourth Sunday services at 11 a.m. For more information, call Carnell Mickens at 919-920-6797 or 215-470-1162.
Mount Nelson Missionary Baptist Church, 206 W. Main St./N.C. 222, Eureka, will have breakfast 9 a.m. to noon March 16 in the fellowship hall. The guest speaker will be April Wilson, who also sings with Servant's Heart. For more information, call 919-242-5996.
Bethel Light Free Will Baptist Church, 2499A U.S. 117 S., will have Restoring the Glory Conference 7 p.m. Wednesday with pastor Jerry Harris; Thursday, apostle Diana McIntyre and Christ Memorial; and March 15, apostle Frank Dawson and Alpha and Omega Christian Center.
ZOAE Christian Center Prosperity School, 101 Ormond Ave., will have a series titled "Father, Where is My Money?" on Fridays beginning 7 p.m. today. For more information, call 919-988-9240.
Greater St. Luke UHCA, 310 W. South St., Rose Hill, will host an appreciation service honoring first lady elder Vickie Flow 4 p.m. Sunday. The guest minister will be elect lady elder Sharon Pickett, first lady of St. John UHCA, Burgaw, and St. Delight UHCA, LaGrange. For more information, call Lashawnda W. Hall at 910-289-0820.
Mount Calvary Missionary Baptist Church, 318 Denmark St., will have church school 9:30 a.m. and worship 10:45 a.m. Sunday. Pastor Winford Galmon Jr. will deliver the message. The annual Missionary Day service will be 3 p.m. Sunday. The guest preacher will be the Rev Marivn Alexander. Bible study will be 6:30 p.m. Wednesday.
Greater Guiding Star United Holy Church will have corporate prayer 9 a.m., Sunday school 10 a.m. and a pastoral service 11 a.m. Sunday. Pastor Joseph Williams will deliver the message. Voices of Praise will provide music. Pastor Williams and Greater Guiding Star will render services 7 p.m. Tuesday at Holly Grove Free Will Baptist Church.
Eureka United Methodist Church, 128 N. Church St., Eureka, will have Sunday school 9:45 a.m. and worship with pastor Connie Belmore 10:45 a.m. Sunday. The youth group will meet 5 p.m. Sunday. Bible study will be 7 p.m. Sunday. The United Methodist women's group will meet 7 p.m. Monday. The prayer group will meet 10 a.m. Tuesday.
New Greenleaf Church of Christ will celebrate Dr. Dorothy Heath's ninth pastoral anniversary 2 p.m. Saturday. The guest preacher will be Dr. Evelena Oliver of St. Jude Church of Christ DOC, Warsaw.
Greenleaf Christian Church (DOC) will have Sunday school 9 a.m. and worship 10 a.m. Sunday. Bishop William J. Barber II will proclaim the word. The praise team will render music, accompanied by the Rev. Ronzel Bell, organist.
St. James Church of Christ, Fremont, will have Sunday school 9:45 to 10:45 a.m. and pastor Tony Sutton's 10th anniversary service 11 a.m. Sunday. The guest speaker will be pastor George Ward of Greater Zion Original Free Will Baptist Church, Stantonsburg. The St. James combined choir will sing. A fellowship meal will be served after the service.
Pastor Ha' Neefa Best will be the speaker 10:30 a.m. Sunday at Salvation Deliverance and Healing, 211 W. Pine St. Pastor Will Best will be the guest speaker 3 p.m. Sunday for Bread of Heaven United Holy Church's anniversary.
"Max Out the Max," a rally for youth in middle school and high school, will be 5 to 7:30 p.m. March 31 at the Maxwell Center. The speaker will be Jon Jorgenson. The rally will include games, inflatables, giveaways, Dance for Christ, a glow party and live music. For more information, call 919-330-8503.
Philadelphia Community Church, 1214 Parkway Drive, will have Sunday school 9:30 a.m. and worship 10:30 a.m. Sunday. Prophet Rodger L. Taylor Jr. will bring the message. The praise team will provide music. Prayer will be 6 p.m. Tuesday. Bible enrichment will be 7 p.m. Tuesday.
New Bethel Church of Fremont will have Holy Communion 6 p.m. Saturday. Guests will include Doris Kornegay of New Daniel Church, Fremont. Sunday school will be 9:45 a.m. and quarterly meeting 11 a.m. Sunday. Pastor Lionel Moore and the choir will render the service. Bible study will be 7 p.m. Thursday.
Gospel Light United Holy Church, 442 E. Hillsboro St., Mount Olive, will have intercessory prayer 9:30 a.m., Bible church school 9:45 a.m. and worship 11:15 a.m. Sunday. Dr. Dwight Morrisey Sr. will deliver the message. The gospel choir will sing. Potluck supper will be 6 p.m. Wednesday. Midweek service will be 7 p.m. Wednesday. Elder Emma Simmons will deliver the message.
Goldsboro Chapel Free Will Baptist Church, 1314 Ben Brewington Court, will have prayer and praise 6 to 7 p.m. today. Sunday school will be 9:45 a.m. and worship 11 a.m. Sunday. Pastor James E. Collins will bring the word. The senior choir will sing. The annual home mission NWB baby contest service will be 6 p.m.
Mount Pleasant Missionary Baptist Church, 4460 U.S. 13 N., will have Sunday school 9:45 a.m. and a Family and Friends Day worship service 11 a.m. Sunday. Minister Jannis Scales of Antioch Missionary Baptist Church will deliver the sermon. The gospel choir will sing. The attire will be casual denim with white blouse or shirt. Dinner will be served after the morning service. Bible study will be 7 p.m. Wednesday.
Barnes Chapel Church, 108 Rosewood Road, will have Sunday school 9:45 a.m. and worship 11 a.m. Sunday. The Rev. Larry Johnson will preach. The choir will sing.
First Baptist Church of Fremont will have service 11 a.m. Sunday. The Rev. John T. Forbes will preach. Brother Charles Fuller will render the music.
Central Heights Free Will Baptist Church, 302 Ervin Drive, will have pre-homecoming cleanup day Saturday morning at the church. Sunday school will be 9:30 a.m. and worship 11 a.m. Sunday. Dr. Isaac Burnett Jr. will deliver the message. Choir No. 1 will provide music. Bible study will be 11:30 a.m. Wednesday.
Holy Temple United Holy Church, 891 Dollard Town Road, will celebrate its 55th anniversary 11 a.m. Sunday with pastor Marlene Duncan and 3 p.m. with guest speaker Dr. Douglas Sutton and Tabernacle of Prayer for All People.
Darden Chapel OFW Baptist Church, 111 Hooks River Road, will have Sunday school 9:30 a.m. and a pastoral service 10:45 a.m. Sunday. Dr. Jerrelle Jones will preach. The mass choir will sing. Women's conference will be 7 p.m. Friday. Evangelist Doris Lewis will preach. Dr. Evelena Oliver, Warsaw, will speak Saturday. Noonday prayer will be Tuesday. Bible study will be 6 p.m. Thursday.
True Holiness House of Prayer Church, 500 Stronach St., will have a Joy Night service 7:30 p.m. Saturday. Sunday school will be 10:15 a.m. and praise and worship 11 a.m. Sunday. Guests will include bishop Curtis Mosely Sr. and New Hope Apostolic Church of Deliverance, Rose Hill. Bible study will be 7:30 p.m. Tuesday.
Liberty Grove Missionary Baptist Church, 2704 N.C. 903 S., LaGrange, will have "Pack the Pew" Family and Friends Day service 3 p.m. Sunday. Guests will include pastor David Howell and the choir, ushers and congregation of Greater Mount Zion Missionary Baptist Church, Kinston. Refreshments will be served.
St. Luke Church of Christ, 430 E. Elm St., will have Sunday school 9:30 a.m. and worship 11 a.m. Sunday. The church will be honoring pastor David Williams' 15th anniversary. Pastor Matthew McNair and Alum Springs Church of Christ, Dover, will be guests. Spring revival services will be 7 p.m. Tuesday, Wednesday and Thursday. The guest evangelist will be pastor Mark T. Sutton form St. James Church of Christ, Fremont. Bible study will be noon and 6 p.m. Wednesday.
Best Grove Missionary Baptist Church will have Sunday school 9:30 a.m. and worship 11 a.m. Sunday. Pastor Joe A. Jackson will preach. The senior choir will sing. The men's fellowship breakfast will be 8 a.m. Saturday. Tutoring will be 5 p.m. Monday. Bible study will be 11 a.m. Tuesday and 7 p.m. Wednesday.
Woods Chapel United American Free Will Baptist Church, 928 New Hope Road, will have Sunday school 9:30 a.m. and a Youth Day service 11 a.m. Sunday. Pastor elder Leo Deans will preach. The youth choir will sing. Jaylen Dawkins will represent Woods Chapel 6 p.m. Sunday in the NWB home mission baby/youth contest at Goldsboro Chapel Free Will Baptist Church. Bible study will be 6 p.m. Wednesday.
Bread of Heaven United Holy Church will have intercessory prayer 9:30 a.m., Sunday school 9:45 a.m. and a Pastoral Day service 11 a.m. Sunday. Elder Charlie Mitchell will deliver the message. The 27th church anniversary service will be rendered by pastor Will Best along with Salvation Healing and Deliverance Ministries at 3 p.m. For more information, call 919-288-9115.
Parker's Chapel will celebrate its 57th church homecoming anniversary 7:30 p.m. Monday with pastor Nick Worrells and One Church; Tuesday, apostle Micheal Artis and St. John; Wednesday, pastor Corey Everette and Mount Airy/Turner Swamp; Thursday, Dr. Louis Leigh and First African Missionary Baptist Church; March 15, Youth Night, pastor Michael Johnson and Ebenezer Missionary Baptist Church; and 11 a.m. March 17, elder Douglas Bell.


text:
\subsection{Motive of the Springer Fiber}
Let $G$ be a connected reductive algebraic group over an algebraically closed field $k.$ Denote by $\nil\subset \g=\operatorname{Lie}(G)$ the associated nilpotent cone and by $\mu:\rnil\rightarrow\nil$ the Springer resolution.
For $N\in\nil$, denote by $\B{N}=\mu\inv(N)\subset\rnil$ the Springer fiber.

Let $\Lambda$ be some commutative ring of coefficients.
Denote by $\DM(\Spec(k), \Lambda)$ the triangulated category of Voevodsky motives over the base field $k$ with coefficients in $\Lambda$ (see \cite{MVW})
\begin{theorem}[Springer Fiber is Pure Tate]\label{thm:pureTate}
The motive of the Springer fiber $\M(\B{N})\in\DM(\Spec(k),\Lambda)$ is pure Tate, that is, a direct sum of Tate motives $\Lambda(n)[2n]$ for $n\geq 0$, if either $\chara k=0$ or if $p=\chara k>0$ and the following three conditions hold:
\begin{enumerate}
\item  $p$ is a good prime for every classical group appearing as a constituent of $G.$
\item  $p>3(h+1)$, where $h$ denotes the maximum of all Coxeter numbers of exceptional constituents in $G.$
\item $p$ is invertible in $\Lambda$ or $\Spec(k)$ admits resolutions of singularities.

\end{enumerate}
\end{theorem}
\begin{remark}
(1) Springer fibers for classical groups admit an affine paving. This is shown in \cite[Theorem 3.9]{DLP} for $\chara k=0$ and generalized in \cite[Chapter 11]{JanNil} to $p=\chara k>0$ for good primes $p$. The existence of an affine paving almost immediately implies that  $\M(\B{N})$ is Tate.

(2) For exceptional groups, the existence of an affine paving is not known. However, DeConcini--Lusztig--Procesi \cite{DLP} show a slightly weaker result, namely that for $k=\C$ the Borel--Moore-homology of $\B{N}$ is torsion free, concentrated in even degrees and generated by algebraic cycles. We show how to adapt their arguments to prove that $\M(\B{N})$ is pure Tate in this case, under the assumption on $\chara(k).$

(3) The last assumption on $\Lambda$ and $p$ ensures a good behavior of motives of singular varieties in $\DM(\Spec(k),\Lambda)$, see \cite{SKA}. For example, it guarantees the existence of the localization triangle.
\end{remark}
\subsection{Equivariant Springer Motives} Now let $k=\overline{\mathbb{F}}_p.$
In \cite[Chapter II]{SoeWeVir} Soergel--Virk--Wendt construct a mixed version of the Bernstein--Lunts equivariant derived category using motivic sheaves. To a linear group $H$ acting on a variety $X\in \Var_k$ with finitely many orbits they associate a $\Q$-linear tensor triangulated category of \emph{$H$-equivariant orbitwise mixed Tate motives} $\MTDer{H}{X}.$
We use this formalism to define the category of \emph{$H$-equivariant Springer motives}
$$\MTSpring{H}{\nil}\defi\langle\mu_*(\un_{\rnil})(n)\,|\, n\in \Z \rangle_{\Delta}\subset\MTDer{H}{\nil}$$
as full triangulated subcategory of $\MTDer{H}{\nil}$ generated by the \emph{Springer motive} $\mu_*(\un_{\rnil})$ and its Tate twists. Here $H$ denotes $G$ or $G\times \Gm,$ acting on $\nil$ in the natural way.

We will show
\begin{theorem}[Motivic Derived Springer Correspondence]\label{thm:motdersprin} There is an equivalence of categories
$$\MTSpring{H}{\nil}\cong \Derb(\rmodulesZ(\Chow_H^\bullet(Z,\Q),\star))$$
between the category of $H$-equivariant Springer motives and the derived category of finitely generated graded right modules over $(\Chow_H^\bullet(Z,\Q),\star).$
\end{theorem}
Here $Z=\rnil\times_{\nil}\rnil$ denotes the Steinberg variety. Furthermore, $(\Chow_H^\bullet(Z,\Q),\star)$ denotes the $H$-equivariant Chow groups of $Z$ equipped equipped with the convolution product
$$c\star c^\prime = (p_{13})_*\left(p_{12}^*(c)\cap p_{23}^*(c^\prime)\right),\text{ for } c,c^\prime\in \Chow^\bullet_H(Z,\Q),$$ where $p_{ij}$ denote the projection maps of the triple product $\rnil\times_{\nil}\rnil\times_{\nil}\rnil.$ Using the explicit description of $(\Chow_H^\bullet(Z,\Q),\star)$ (see for example \cite{Chowringsteinberg}) this yields
\begin{corollary} There are equivalences of categories
\begin{align*}
\MTSpring{G}{\nil}&\cong \Derb(\rmodulesZ\Q[W]\#\Sym^\bullet(X(T)))\text{ and}\\
\MTSpring{G\times \Gm}{\nil}&\cong \Derb(\rmodulesZ\overline{\mathbb{H}}).
\end{align*}
Here $X(T)$ denotes the character group of a maximal torus $T\subset G$, $W$ the Weyl group of $G$ and $\Q[W]\#\Sym^\bullet(X(T))$ the semidirect product of the group algebra of $W$ with the symmetric algebra of $X(T).$ Furthermore $\overline{\mathbb{H}}$ denotes the \emph{graded affine Hecke algebra} associated to $G$ as defined by Lusztig \cite{MR991016}.
\end{corollary}
\subsection{Relation To Other Work}
The second half of this paper is a motivic version of the \emph{derived Springer correspendence} as constructed by Rider \cite{LR1} in the context of equivariant mixed $\ell$-adic sheaves. The motivic setup, as very recently introduced by Soergel--Wendt--Virk \cite{SoeWeVir}, has certain advantages. First, there are no non-trivial extensions between Tate objects, corresponding to the vanishing of rational higher $K$-theory of finite fields and their algebraic closures. Using this, technical difficulties with $\ell$-adic sheaves that necessitate to state the derived Springer correspondence in terms of either dg-categories or the homotopy category of pure complex disappear. Second, Springer motives are defined rationally. Hence all statements are independent of $\ell.$
\subsection{Future Work} (1) In upcoming work with Shane Kelly, generalizing \cite{EKe}, we define a formalism of equivariant motives with coefficients in a finite field. This will allow us to prove a modular motivic derived Springer correspondence analogously. \\\noindent (2) It would be interesting to also consider a generalized motivic derived Springer correspondence along the lines of Rider--Russell \cite{LR2} and \cite{LR3}.\\
(3) Also, it would be interesting to obtain a $K$-theoretic version of the result using equivariant $K$-motives in the sense of Hoyois, see \cite{Hoy1}\cite{Hoy2}. Then it would be possible to handle the affine Hecke algebra. Similar $K$-motivic statements have considered by the author in the case of flag varities \cite{EKo}.

\subsection{Acknowledgements} We thank Rapha\"el Rouquier and Wolfgang Soergel for helpful discussions. We thank George Lusztig for answering a question about \cite{DLP}. Also, we would like to warmly thank the referee for a constructive report.

\subsection{Tate motives} We state some general results on pure Tate motives.
\begin{definition} A motive $M\in\DM(\Spec(k), \Lambda)$ is called \emph{pure Tate} if it is isomorphic to a finite direct sum of Tate motives of the form $\Lambda(n)[2n].$
\end{definition}
\begin{definition} Let $X\in \Var_k.$ An \emph{$\alpha$-partition} of $X$ is a finite family of subvarieties  $X_1,\dots, X_s$ of $X$ such that $\bigcup_{i=1}^r X_i$ is closed in $X$ for all $1\leq r\leq s.$ If each $X_i$ is furthermore isomorphic to some affine space $\A^n$, we call the \emph{$\alpha$-partition} an \emph{affine paving} of $X.$
\end{definition}

\begin{lemma} Let $X,Y\in \Var_k$ and $E\rightarrow X$ a vector bundle of rank $r.$\label{lem:puretategeneral}
\begin{enumerate}
\item There is an isomorphism $\Lambda(p)[2p]\otimes\Lambda(q)[2q]\cong \Lambda(p+q)[2(p+q)].$
\item If $X$ is proper, then $M^c(X)=M(X).$
\item\label{lem:puretategeneral:kuen} There is an isomorphism $M(X\times Y)=M(X)\otimes M(Y)$ and if $M(X)$ and $M(Y)$ are pure Tate, then so is $M(X\times Y).$
\item There is an isomorphism $M^c(X\times Y)=M^c(X)\otimes M^c(Y)$ and if $M^c(X)$ and $M^c(Y)$ are pure Tate, then so is $M^c(X\times Y).$
\item There is an isomorphism $M^c(E)\cong M^c(X)(r)[2r]$ and $M^c(X)$ is pure Tate if and only if  $M^c(E)$ is pure Tate.
\item There is an isomorphism $$M^c(\Proj(E))\cong \bigoplus_{p=0}^{r-1}M^c(X)(p)[2p]$$ and $M^c(X)$ is pure Tate if and only if  $M^c(\Proj(E))$ is pure Tate.
\item Let $X$ be smooth and $Z\subset X$ be a closed smooth subvariety of codimension $c$. Denote the the blow-up of $X$ along $Z$ by $\Bl_Z(X).$ Then
 $$M(\Bl_Z(X))\cong M(X)\oplus\bigoplus_{p=1}^{c-1}M(Z)(p)[2p]$$
 and $M(X)$ and $M(Z)$ are pure Tate if and only if $M(\Bl_Z(X))$ is pure Tate.
\item If $Z\subset X$ is a closed subvariety and $U=X \backslash Z.$ Then there is a distinguished triangle, called localisation triangle,
\begin{center}
\disttriangle{M^c(Z)}{M^c(X)}{M^c(U)}
\end{center}
and $M^c(X)$ is pure Tate if and only if $M^c(Z)$ and $M^c(U)$ are pure Tate.
\item If $X_1,\dots, X_s$ is an $\alpha$-partition of $X$, then  $M^c(X)$ is pure Tate if and only if $M^c(X_i)$ is pure Tate for all $i.$
\item If $X$ has an affine paving, then $M^c(X)$ is pure Tate.
\end{enumerate}
\end{lemma}
\begin{proof}
(1)-(7) Can be found in \cite[Sections 14-16]{MVW}.
\\ \noindent (8) To show that $M^c(X)$ is pure Tate if $M^c(Z)$ and $M^c(U)$ are, we claim that
the boundary map $M^c(U)\rightarrow M^c(Z)[1]$ in the localisation triangle vanishes. Let $\Lambda(q)[2q]$ and $\Lambda(p)[2p]$ be direct summands of $M^c(U)$ and $M^c(Z)[1]$, respectively. Then
\begin{align*}
\Hom{\DM(\Spec(k),\Lambda)}{\Lambda(q)[2q]}{\Lambda(p)[2p+1])}
&=\Chow^{p-q}(\Spec(k),-1)\otimes \Lambda=0
\end{align*}
where the right hand side denotes a higher Chow group which vanishes since in general $\Chow^\bullet(-,-1)=0.$
Hence $M^c(X)=M^c(Z)\oplus M^c(U)$ and the statement follows.
\\ \noindent (9) Follows by (8) and induction.
\\ \noindent (10) Follows from $M^c(\A^n)=\Lambda(n)[2n]$ and (9).
\end{proof}
As demonstrated in \cite{BBB}, there is a Bia\l{}ynicki-Birula decomposition of motives of varieties with $\Gm$-actions. This can sometimes be used to show that a smooth projective variety is pure Tate.
\begin{lemma}\label{lem:bbstrat}
Let $X\in \Var_k$ be a smooth projective variety equipped with an action of $\Gm.$ Then $M(X^\Gm)=M^c(X^\Gm)$ is pure Tate if and only if $M(X)=M^c(X)$ is.
\end{lemma}
\begin{proof} The Bia\l{}ynicki-Birula theorem gives an $\alpha$-partition of $X$ into vector bundles on the connected components of $X^\Gm.$ The statement follows using the previous lemma.
\end{proof}
\subsection{Prehomogeneous Vector Spaces and Pure Tateness}\label{subsec:prehom}
We show how the methods of \cite[Section 2]{DLP} allow to prove that a certain variety associated to a prehomogeneous vector space is pure Tate. We recall some of their notation.

Let $M$ be a connected linear algebraic group and $V$ a prehomogeneous $M$-module, that is, $V$ contains a dense $M$-orbit $V^0.$ Fix a $v\in V^0$ and denote by $M_v$ its stabilizer in $M.$ Let $H$ be a closed Borel-subgroup in $M$ and $U$ an $H$-stable linear subspace of $V.$ Let
\begin{align*}
M_U&=\{g\in M\,|\, g^{-1}v\in U\} \text{ and}\\
X_U&=M_U/H.
\end{align*}
We are interested in the motive of the varieties $X_U.$ By \cite[Lemma 2.2(i)]{DLP} and since $H$ is a Borel subgroup, $X_U$ is a smooth projective variety.

Let $\Gamma$ be the set of $H$-stable subspaces of $V.$ For $U\in\Gamma$, let $P_U$ be the stabilizer of $U$ in $M$ and denote
$\delta(U)=\dim(M/P_U)-\dim(V/U)$ and $\gamma(U)=\dim(M/H)-\dim(V/U).$
In \cite[Section 2.7]{DLP}, $\Gamma$ is equipped with the structure of a directed graph, whose edges $(U, U^\prime)$ have the property
\begin{enumerate}
\item $U\subset U^\prime$,
\item $\dim U^\prime/U=1$ and
\item there exists a parabolic subgroup $P\supset H$ of semisimple rank 1 and $U^{\prime\prime}\in \Gamma$ such that $U^{\prime\prime}\subset U$, $P\subset P_{U^{\prime\prime}}$, $P\not\subset P_U$, $P\subset P_{U^\prime}$ and $\dim U/U^{\prime\prime}=1.$
\end{enumerate}
 Then, the $M$-module $V$ is called \emph{good} if for any $U\in \Gamma$ either $U\subset U^\prime$ for some $U^\prime\in \Gamma$ with $\delta(U^\prime)<0$, or $U$ lies in the same component of $\Gamma$ as some $U^\prime\in\Gamma$ with $\delta(U^\prime)\leq 0.$

 In \cite[Proposition 2.12]{DLP} it is then shown that under the condition that $V$ is good the Borel--Moore-homology of $X_U$ is torsion free, concentrated in even degrees and generated by algebraic cycles. We copy their arguments and show that $M(X_U)$ is pure Tate.

 \begin{proposition}\label{prop:goodTate} Assume that the $M$-module $V$ is good. Then $M(X_U)$ is pure Tate for all $U\in \Gamma.$
 \end{proposition}
 \begin{proof}
To translate the inductive argument used in \cite{DLP} to the world of motives, we will use the slice filtration $\nu$ for effective motives as studied in \cite{huka}.

To any $X_U$, this associates a family of objects $\nu_{<n}M(X_U)$ for $n\geq 0$ and a family of compatible morphisms $\nu_{<n}M(X_U)\rightarrow\nu_{<m}M(X_U)$ for $n\geq m.$ By definition $\nu_{<0}M(X_U)=0$ and since $X_U$ is a smooth projective variety by \cite[Propositions 1.7, 1.8]{huka} we have $\nu_{<n} M(X_U)=M(X_U)$ for $n>\dim X_U$.

Hence it suffices to show that $\nu_{<n}M(X_U)$ is pure Tate for all $n.$ For each $U\in \Gamma$ and $n\geq 0$ consider the following statement
\begin{enumerate}
\item[$(PT_n)$] $\nu_{<n}M(X_U)$ is pure Tate.
\end{enumerate}
We prove this by induction on $n.$ If $n=0$, then $\nu_{<n}M(X_U)=0.$
Now let $n\geq 1$ and assume that $(PT_{n-1})$ holds for all $U\in\Gamma.$

If $U\in\Gamma$ is contained in $U^\prime\in\Gamma$ with $\delta(U^\prime)<0$, then $X_U$ is empty and hence $M(X_U)=0$ pure Tate. If $\delta(U)\leq 0$, then $X_U$ is a finite disjoint union of flag varieties isomorphic to $P_U/H$ by \cite[Paragraph 2.9 (a)]{DLP}. The Bruhat decomposition provides an affine paving of $P_U/H.$ Hence  $M(X_U)$ is pure Tate by Lemma \ref{lem:puretategeneral}.

Since $V$ is good, for each connected component of $\Gamma$ there is hence some $U$ for which $(PT_n)$ holds. So the statement of the proposition reduces to the following lemma.
  \end{proof}
\begin{lemma}
Assume that $n\geq 1$ and $(PT_{n-1})$ holds for all $U_1\in\Gamma.$ Let $U\subset U^\prime$ be an edge in $\Gamma.$ Then  $(PT_n)$ holds for $U$ if and only if $(PT_n)$ holds for $U^\prime.$
\end{lemma}
\begin{proof}
Let $U^{\prime\prime}$ and $P$ as in property (3) of edges of $\Gamma.$
Let
$$Z =\{(gH, g^\prime H) \in  M/H\times M/H \,|\, g^{-1}v\in U \text{ and } g^{-1}g^\prime\in P\}.$$
Then by \cite[Lemma 2.11]{DLP} $Z\rightarrow X_U$ is the projectivization of a vector bundle of rank two $E\rightarrow X_U$ and furthermore $Z\cong \Bl
_{X_{U^{\prime\prime}}}(X_{U^\prime})$, where $X_{U^{\prime\prime}}\subset X_{U^\prime}$ is a closed subvariety of codimension two. Hence by the projective bundle and blow-up formula we have
$$
M(X_U)\oplus M(X_U)(1)[2]=M(Z)=M(X_{U^\prime})\oplus M(X_{U^{\prime\prime}})(1)[2].
$$
Applying $\nu_{<n}$ yields that
$$ \nu_{<n}\left(M(X_U)\oplus M(X_U)(1)[2]\right)=\nu_{<n}(M(X_U))\oplus \nu_{<n-1}(M(X_U))(1)[2]$$
equals
$$ \nu_{<n}\left(M(X_{U^\prime})\oplus M(X_{U^{\prime\prime}})(1)[2]\right)=\nu_{<n}(M(X_{U^\prime}))\oplus \nu_{<n-1}(M(X_{U^{\prime\prime}}))(1)[2]$$
where we use that $\nu_{<n}(-(1))=\nu_{<n-1}(-)(1)$, see \cite[Corollary 1.4(v)]{huka}.
Now $\nu_{<n-1}(M(X_{U^{\prime\prime}}))$ and $\nu_{<n-1}(M(X_U))$ are pure Tate by induction, and the Statement follows.
\end{proof}
\subsection{Springer Fiber is Pure Tate} We prove Theorem \ref{thm:pureTate} from the introduction. Let $G$ be reductive algebraic group over $k$, $N\in \nil\subset \g$ be an element of the nilpotent cone in the Lie algebra of $G$ and $\B{N}=\mu\inv(N)\subset\rnil$ the Springer fiber in the Springer resolution $\mu: \rnil\rightarrow\nil.$  Let $$\B{}=\{\borel\subset \g \,|\, \borel \text{ is a Borel subalgebra}\}$$ denote the flag variety. Then we can identify
$$\B{N}=\{\borel\subset \g \,|\, N\in \borel\}\subset\B{}.$$
The goal is to prove that $M(\B{N})\in \DM(\Spec(k),\Lambda)$ is pure Tate. We note that the Springer fiber is proper and hence $M^c(\B{N})=M(\B{N}).$

As the Springer fiber only depends on the isogeny class of the semisimple part of $G,$ we may assume that $G$ is of adjoint type and hence a direct product of its simple constituents (see \cite[Section 2.7]{JanNil}).
Furthermore, a Springer fiber of a direct product of groups decomposes into a direct product as well, and by Lemma \ref{lem:puretategeneral}(\ref{lem:puretategeneral:kuen}) it suffices to consider each individual factor.

So we can assume that $G$ is a simple algebraic group. If $G$ is a classical group, that is, of type $A,B,C$ or $D,$ then $\B{N}$ admits a paving by affine spaces  by \cite{DLP} if $\chara(k) =0$ and more general by \cite[Theorem 11.22]{JanNil} if $p=\chara(k)$ is good for $G.$ Hence $M(\B{N})$ is pure Tate in this case by Lemma \ref{lem:puretategeneral}.

We can hence assume that $G$ is a simple group of exceptional type $E, F$ or $G$ and assume that $p>3(h+1)$, where $h$ denotes the Coxeter-number of $G.$
We proceed as in \cite[Section 3.4]{DLP}.

There exists a special cocharacter $\tau: \Gm\rightarrow G$ associated to $N$, see  \cite[Section 5.2]{JanNil} for a definition and existence and uniqueness result, alternatively use the Morozov--Jacobson theorem, which holds since $p>3(h-1)$. This cocharacter induces a decomposition of $\g$ into even weight spaces
 $$\g=\bigoplus_{n\in\Z} \g(2n, \tau),$$
 such that $N\in \g(2,\tau).$ Let $G_0\subset P\subset G$ be the Levi and parabolic subgroup with Lie algebra $\g(0,\tau)$ and $\bigoplus_{n\geq 0}\g(2n, \tau)$, respectively, and let $S=\tau(\Gm).$
Now $\B{N}$ admits an $\alpha$-filtration by intersecting it with the $P$-orbits $\mathcal O$ on $\B{}.$ Each of those intersections $\B{N,\mathcal O}=\B{N}\cap \mathcal O$ is smooth projective.

So $\M(\B{N})$ is pure Tate if and only if $M(\B{N,\mathcal O})$ is pure Tate for each $\mathcal{O}$ by Lemma \ref{lem:puretategeneral}.
Furthermore each  $M(\B{N,\mathcal O})$ is pure Tate if and only if $M(\B{N,\mathcal O}^S)$ is pure Tate by Lemma \ref{lem:bbstrat}.

By a similar argument to \cite[Section 3.6]{DLP} and using  Lemmata \ref{lem:puretategeneral}, \ref{lem:bbstrat} again, we can reduce to the case that $N$ is in fact a distinguished nilpotent element, so not already contained in the Lie algebra of any proper Levi subgroup of $G.$

Let $B_0\subset G_0$ be a Borel subgroup. Denote its Lie algebra by $\borel_0.$ Then there is a unique $\borel_\mathcal{O}\in \mathcal{O}^S$ with $\borel_\mathcal{O}\cap \g(0,\tau)=\borel_0.$ Let $U_\mathcal{O}=\borel_\mathcal{O}\cap \g(2,\tau).$ This is a $B_0$-stable linear subspace of the prehomogeneous $G_0$-module $\g(2,\tau).$ We can hence consider the variety $X_{U_\mathcal{O}}$ as defined in Section \ref{subsec:prehom}. In fact the map $X_{U_\mathcal{O}}\rightarrow \B{N,\mathcal O}^S, \,gB_0\mapsto g\borel_\mathcal{O}$ is an isomorphism.

Now \cite{DLP} show by an involved case by case computation that the $G_0$-modules $\g(2,\tau)$ arising in this way from a distinguished nilpotent element for an exceptional group are \emph{good.} This computation, as the whole paper, is carried out for $k=\C$ but also works as long as the Morozov--Jacobson theorem holds, so in particular if $p>3(h-1).$ We thank George Lusztig for answering a question about that. We can hence use Proposition \ref{prop:goodTate} to see that $M(X_{U_\mathcal{O}})=M(\B{N,\mathcal O}^S)$ is pure Tate.

This concludes the proof of Theorem \ref{thm:pureTate}.

\subsection{Orbitwise Pure Tateness of the Springer motive} In the introduction we cheated a bit. A priori, it is not clear that the Springer motive $\mu_!(\un_{\rnil})=\mu_*(\un_{\rnil})\in \DerG{H}{\nil}$ already lives in the subcategory $\MTDer{H}{\nil}.$ In this section we show how the pure Tateness of the Springer fiber implies this and that $\mu_!(\un_{\rnil})$ is additionally pointwise pure.
\begin{theorem} Let $\mathbb{O}$ be an $H$-orbit on $\nil$. Let $N$ be a point in $\mathbb{O}$ and denote by $H_N\subset H$ its stabilizer.
Denote the corresponding morphisms of varieties with group action by
\begin{align*}
\mu=(\id,\mu):(H\looparrowright \rnil)&\rightarrow (H\looparrowright\nil),\\
j=(\id,j):(H\hookrightarrow\mathbb{O})&\hookrightarrow (H\looparrowright\nil)\text{ and}\\
(\iota,i):(H_N\looparrowright \{N\})&\hookrightarrow (H\looparrowright\mathbb{O}).
\end{align*}
Then for $?\in\{*,!\}$ we have a chain of functors
\begin{center}
\begin{tikzcd}
\DerG{H}{\rnil}\arrow{r}{\mu_!=\mu_*}&\DerG{H}{\nil}\arrow{r}{j^?}&\DerG{H}{\mathbb{O}}\arrow{r}{(\iota,i)^*}&\DerG{H_N}{\{N\}}\arrow{r}{\For}&\DerG{}{\Spec(k)}
\end{tikzcd}
\end{center}
where $\For$ is the functor forgetting the $H_N$ action.
We claim that
$$\For(\iota,i)^*j^?\mu_!(\un_{\rnil})\in\DerG{}{\Spec(k)}$$
is pure Tate, that is, a finite direct sum of Tate motives $\un(n)[2n].$
\end{theorem}
\begin{proof} Since the forgetful functor $\For$ commutes with all six functors, it suffices to show the corresponding statement where we forget about all group actions. Since $\mu$ is proper and hence $\mu_*=\mu_!$, it suffices to show the statement for $?=*$ by duality. Now we apply base change for the cartesian diagram
\begin{center}
\begin{tikzcd} \B{N}=\mu^{-1}(N) \arrow{r}{k}  \arrow{d}{\fin_{\B{N}}}   &  \mu^{-1}(\mathbb{O}) \arrow{r}{l} \arrow{d}{}& \rnil \arrow{d}{\mu} \\

\Spec(k)=\{N\}  \arrow{r}{i} &  \mathbb{O} \arrow{r}{j} & \nil
	\end{tikzcd}
\end{center}
and see that
  $$\For(\iota,i)^*j^*\mu_!(\un_{\rnil})\cong\fin_{\B{N},!}(k^*l^*\un_{\rnil})=\fin_{\B{N},!}(\un_{\B{N}})\in\DerG{}{\Spec(k)}.$$
Since we are working with rational coefficients there is a natural equivalence $$\DerG{}{\Spec(k)}=\DA(\Spec(k),\Q)\cong \DM(\Spec(k),\Q),$$ see \cite{Ayoubetale}, and the Verdier dual of $\fin_{\B{N},!}(\un_{\B{N}})\in\DerG{}{\Spec(k)}$ corresponds to  $M^c(\B{N})\in\DM(\Spec(k),\Q)$, the motive of the Springer fiber. But $M^c(\B{N})$ is pure Tate by Theorem \ref{thm:pureTate}.
\end{proof}
 By definition, $\MTDer{H}{\nil}$ consists of motives $M$ such that $$\For(\iota,i)^*j^?M\in\left\langle \un(n) \,|\,n\in\Z\right\rangle_\Delta\subset\DerG{}{\Spec(k)}$$ is mixed Tate, i.e. contained in the triangulated category generated by motives $\un(n)\in \DerG{}{\Spec(k)},$ for each orbit $j:\mathbb{O}\hookrightarrow \nil, ?\in\{*,!\}$ and $(\iota,i)^*$ defined as above. A motive $M$ is called \emph{pointwise $?$-pure} if additionally  $\For(\iota,i)^*j^?M$ is pure Tate  (so a finite direct sum of motives $\un(n)[2n]$) for $?\in\{*,!\}$ and \emph{pointwise pure} if it is pointwise $*$-pure and pointwise $!$-pure.
\begin{corollary} We have $\mu_*(\un_{\rnil})\in\MTDer{H}{\nil}$ and $\mu_*(\un_{\rnil})$ is pointwise pure.
\end{corollary}
\subsection{Tilting and Formality for Springer motives}
Denote by
$$\MTSpring{H}{\nil}_{add}=\left\langle \mu_*(\un_{\rnil})(n) \,|\, n\in \Z\right\rangle_{\oplus, \inplus}\subset \MTSpring{H}{\nil}$$
the idempotent closed additive subcategory of $\MTSpring{H}{\nil}$ generated by the Springer motive and its Tate twists.
\begin{lemma}\label{lem:springtilt}
The category $\MTSpring{H}{\nil}_{add}$ is a \emph{tilting subcategory} of $\DerG{H}{\nil},$ meaning that it is
\begin{enumerate}
\item  idempotent closed, additive and
\item $\Hom{\DerG{H}{\nil}}{M}{N[i]}=0$ for all $M,N\in  \MTSpring{H}{\nil}_{add}$ and $i\neq 0.$
\end{enumerate}
  \end{lemma}
  \begin{proof} (1) Holds by construction.\\\noindent (2) This is implied by the pointwise purity of the objects in $\MTDer{H}{\nil}_{add}$ using an argument very similar to \cite[Corollary 6.3]{SoeWe}.  More, generally we show that for all $M,N\in\MTSpring{H}{\nil}$ with $M$ pointwise $*$-pure and $N$ pointwise $!$-pure $$\Hom{\DerG{H}{\nil}}{M}{N[i]}=0$$ for $i\neq 0.$ For this, denote by $j: U\hookrightarrow \nil$ and $i:Z=\nil\backslash U\hookrightarrow \nil$ the inclusion of the open orbit and its closed complement. Then the localisation sequence
 \begin{center}
\disttriangle{j_!j^!M}{M}{i_*i^*M}
\end{center}
yields an exact sequence
\begin{center}
\begin{tikzcd}[column sep=small]
 \Hom{\DerG{H}{Z}}{i^*M}{i^!N[i]}\arrow[r] & \Hom{\DerG{H}{\nil}}{M}{N[i]} \arrow[r] & \Hom{\DerG{H}{U}}{j^*M}{j^!N[i]}.
\end{tikzcd}
\end{center}
Now $i^*M$ is pointwise $*$-pure and $i^!N$ is pointwise $!$-pure. Hence, the the left hand side vanishes for $i\neq 0$ by induction (here we use that there are only finitely many orbits). Also, the right hand side vanishes for $i\neq 0$ using the purity assumption, the induction equivalence and that $\Hom{\DerG{H_N}{\nil}}{\Q}{\Q(p)[q]}=0$ unless $p=2q,$ where $H$ denotes the stabiliser of a point $N\in U.$
  \end{proof}
  \begin{remark} The arguments in the proof of Lemma \ref{lem:springtilt} (2) argument do not translate to the non-equivariant case immediately. Hence, it is not clear if a non-equivariant analogue of the motivic derived Springer correspondence is true. One would need to show that the higher Chow groups of nilpotent orbits vanish, which is not clear to the author.
  \end{remark}
  We can now apply the tilting formalism and show
  \begin{theorem}
  There is an equivalence of categories, called \emph{tilting}, between
  $$\tilt: \Hotb(\MTSpring{H}{\nil}_{add})\stackrel{\sim}{\rightarrow}\MTSpring{H}{\nil}$$
  the homotopy category of bounded chain complexes $\MTSpring{H}{\nil}_{add}$ and the category of Springer motives $\MTSpring{H}{\nil}.$
  \end{theorem}
  \begin{proof}
  Since by Lemma \ref{lem:springtilt} $\MTSpring{H}{\nil}_{add}$ is a tilting subcategory of $\DerG{H}{\nil}$ by \cite[Theorem B.3.1]{SoeWeVir}, which establishes a tilting formalism for stable derivators, there is a fully faithful functor
  $$\tilt: \Hotb(\MTSpring{H}{\nil}_{add})\rightarrow\DerG{H}{\nil}.$$
  The essential image of $\tilt$ is the triangulated subcategory of $\DerG{H}{\nil}$ generated by $\MTSpring{H}{\nil}_{add}$ which is $\MTSpring{H}{\nil}$ by definition.
 \end{proof}
We name the $\Z$-graded ``Ext"-algebra\footnote{We put the quotation marks here because of the Tate twists which is not part of the definition of the true Ext-algebra. In fact, the true Ext-algebra is concentrated in degree 0, by Lemma  \ref{lem:springtilt}.} of the Springer motive $\mu_*\left(\un_{\rnil}\right)$
 $$E:=\bigoplus_{n\in\Z} E^n\text{, where }E^n=\Hom{\DerG{H}{\nil}}{\mu_*\left(\un_{\rnil}\right)}{\mu_*\left(\un_{\rnil}\right)(n)[2n]}.$$
 We denote the shift of grading functor for graded $E$-modules by $\langle-\rangle.$
 We can rephrase the last theorem as
 \begin{corollary}
 There is an equivalence of categories
 $$\Derb(\rmodulesZ E)\rightarrow\MTSpring{H}{\nil}$$
 between the bounded derived category of finitely generated graded right modules over $E$ and the category of Springer motives.
 \end{corollary}
 \begin{proof}
 The category $\MTSpring{H}{\nil}_{add}$ can be identified with the full subcategory
 $$\left\langle E\langle n\rangle \,|\, n\in \Z\right\rangle_{\oplus, \inplus}\subset \rmodulesZ E.$$
 of graded right $E$-modules generated by finite direct sums and summand of shifts of $E.$
 By the explicit description of $E$, see the next section, $E$ has finite cohomological dimension, and hence the homotopy category of bounded chain complexes in $\left\langle E\langle n\rangle \,|\, n\in \Z\right\rangle_{\oplus, \inplus}$ is equivalent to the bounded derived category of graded $E$-modules.
 \end{proof}
\subsection{Description of the ``Ext"-algebra $E$} The last step in the proof of Theorem \ref{thm:motdersprin} is to explicitely describe the ``Ext"-algebra $E.$ Recall that $Z=\rnil\times_\nil\rnil$ denotes the Steinberg variety and that $H$ acts on $Z$ by the diagonal action. We repeat some results from \cite[Section 8.6]{crisginz}, who give an explicit description of the sheaf-theoretic version of $E$ in terms of the Borel--Moore homology of the Steinberg-variety. Their results translate to the motivic setting almost word by word, all that is needed is a six-functor formalism.
\begin{lemma}
There is an isomorphism of graded algebras
$$E\cong(\Chow^{\bullet}_H(Z,\Q),\star)$$
between $E$ and the $H$-equivariant Chow groups of $Z$ equipped with the convolution product.
\end{lemma}
\begin{proof}
We just show that $E^n\cong \Chow^{n}_H(Z,\Q)$ as a vector space here. The statements about the algebra structure can be deduced as in \cite[Section 8.6]{crisginz}.
Consider the cartesian diagram of $H$-varieties:
\begin{center}
\cartesiandiagramwithmaps{Z}{p_2}{\rnil}{p_1}{\mu}{\rnil}{\mu}{\nil}
\end{center}
Denote for a variety $X\in\Var_k$ its structure map by $\fin_X:X\rightarrow \Spec(k)=pt.$ Since $\rnil$ is smooth we have $\un_{\rnil}=\fin_{\rnil}^*(\un_{pt})=\fin_{\rnil}^!(\un_{pt})(-d)[-2d]$ where  $d=\dim(\rnil).$ Furthermore note that $\mu$ is proper and hence $\mu_!=\mu_*$. Now consider
\begin{align*}
E^n&=\Hom{\DerG{H}{\nil}}{\mu_!(\un_{\rnil})}{\mu_*(\un_{\rnil})(n)[2n]}\\
&=\Hom{\DerG{H}{\rnil}}{\un_{\rnil}}{\mu^!\mu_*(\un_{\rnil})(n)[2n]}\\
&=\Hom{\DerG{H}{\rnil}}{\un_{\rnil}}{p_{1,*}p_2^!(\un_{\rnil})(n)[2n]}\\
&=\Hom{\DerG{H}{\rnil}}{\fin_{\rnil}^*(\un_{pt})}{p_{1,*}p_2^!\fin_{\rnil}^!(\un_{pt})(n-d)[2(n-d)]}\\
&=\Hom{\DerG{H}{pt}}{\un_{pt}}{\fin_{Z,*}\fin_{Z}^!(\un_{pt})(n-d)[2(n-d)]}\\
&=\Chow^{\dim(Z)+(n-d)}_H(Z,\Q)=\Chow^{n}_H(Z,\Q)
\end{align*}
where in the last equality we used \cite[Theorem II.2.9.]{SoeWeVir} (there is no resolution of singularities for $\Spec(k)$ necessary here, using \cite[Section 5.2]{SKA} and that $p$ is invertible in $\Q$) and that $Z$ is of dimension $\dim(Z)=d.$
\end{proof}

\section{Introduction}
\import{Inhalt/}{Intro.tex}
\section{Motive of the Springer Fiber}
\import{Inhalt/}{MotiveofSpr.tex}
\section{Equivariant Springer Motives}
\import{Inhalt/}{Form.tex}

\bibliographystyle{amsalpha}

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text:
Gerrit Janszoon Vos znany jako Gerardus Joannes Vossius (ur. 1577 w Heidelbergu; zm. 17 marca 1649 w Amsterdamie) – niderlandzki uczony i humanista, wykładowca historii, filozofii, teologii i greki. Autor licznych dzieł z dziedziny historii, retoryki, gramatyki, a także słownika etymologicznego.

Życiorys
Urodził się w Heidelbergu w marcu lub kwietniu 1577 roku. Jego rodzicami byli kupiec i kaznodzieja Joannes Vossius i Cornelia van Buel. Rodzina mieszkała w Heidelbergu od 1571 roku po przeprowadzce z Roermondu, spowodowanej prześladowaniami protestantów. Krótko po jego narodzinach rodzina przeniosła się do Dordrechtu, gdzie jego ojciec został później pastorem. Vos uczęszczał do szkoły łacińskiej w Dordrechcie, a następnie studiował sztukę i teologię w Lejdzie. Przed ukończeniem studiów teologicznych wrócił do Dordrechtu, aby objąć stanowisko rektora w szkole łacińskiej. W 1606 roku opublikował Oratoriae Institutiones, dzieło, które zyskało mu uznanie jako mistrza retoryki. W latach 1615–1619 kierował Collegium Theologicum w Lejdzie. Od listopada 1622 roku wykładał łacinę, literaturę i historię powszechną na Uniwersytecie w Lejdzie. Odrzucił propozycję profesury na Uniwersytecie w Cambridge, ale w 1631 roku przyjął stanowisko pierwszego rektora nowo powstającego Athenaeum Illustre w Amsterdamie. Współpracował tam z humanistą Casparem Barlaeusem, razem brali udział w spotkaniach Muiderkring, zgromadzenia skupiającego literatów i muzyków.

Zmarł w 1649 roku zarażony różą, chociaż podawano także inne okoliczności jego śmierci. Vossius miał po kłótni w księgarni wrócić wzburzony do domu i umrzeć wyczerpany emocjami. Według innej wersji miał zginąć przygnieciony ciężkimi woluminami po tym, jak załamał się pod nim stopień bibliotecznej drabiny.

Jego syn Isaac Voss, erudyta i królewski bibliotekarz, zgromadził imponującą kolekcję książek, którą pośmiertnie przekazał Uniwersytetowi w Lejdzie.

Dzieła
Był jednym z pierwszych uczonych badających dogmaty i niechrześcijańskie religie z punktu widzenia historii. Jego najważniejsze dzieła to:

 De historicis Graecis, libri IV, (1601)
 Commentariorum Rhetoricorum oratoriarum institutionum Libri VI (1606)
 Historiae de controversiis quas Pelagius eiusque reliquiae moverunt (1618)
 Rhetorices contractae sive partitionum oratoriarum libri V (1621)
 Aristarchus, sive de arte grammatica (1635 i 1695; nowe wyd. w 2 tomach, 1833–35)
 Rhetorices contractae sive partitionum oratoriarum libri V (1621)
 De rhetorices natura ac constitutione, et antiquis rhetoribus, sophistis, ac Oratoribus, liber I, (1621)
 Ars historica, sive de historiae & historices natura, historiaeque scribendae preceptis, commentatio, (1623)
 De Historicis Graecis Libri IV (1624)
 De Historicis Latinis Libri III (1627)
 Aristarchus, sive de arte grammatica, (1635)
 Commentatorium rhetoricorum (1630)
 Of Errors of Speech and Latino-Barbarous Terms (1640)
 De Theologia Gentili (1642)
 Latina prosodia, et artis metricae elementa, (1645)
 Dissertationes Tres de Tribus Symbolis, Apostolico, Athanasiano et Constantinopolitano (1642)
 Poeticarum institutionum libri III (1647); nowe wyd. 2006
 De artis poeticae natura ac constitutione liber (1647); nowe wyd. 2006
 De Imitatione Liber (1647); nowe wyd. 2006
 De baptismo Disputationes XX et una de sacramentorum vi atque efficacia, (1648)
 De quatuor artibus popularibus, de philologia et scientiis mathematicis, cui operi subiungitur chronologia mathematicorum. 3. De universae mathesios natura et constitutione liber, cui subjungitur chronologia mathematicorum, (1650)
 De historicis Latini, libri III, (1651)
 The Times of the Ancient Poets (1654)
 Harmoniae evangelicae de passione, morte, resurrectione, ac adscensione Iesu Christi, Servatoris nostri, libri tres, (1656)
 Etymologicum linguae Latinae (1662; nowe wyd. w 2 tomach, 1762–63)
 De theologia gentili et physiologia christiana; sive de origine ac progressu idololatriae, (1662)
 Correspondence of Vossius with Eminent Men (1691)

Jego dzieła zebrane zostały wydane w Amsterdamie (6 tomów, 1695–1701). Jego dzieła o retoryce były bardzo popularne i używane jako podręczniki. Popierał definicje Arystotelesa, a sprzeciwiał się Ramusowi. Największy wpływ wywarli na niego Arystoteles i Cyceron, cytował także Bartłomieja Keckermanna, Menandra, Hermogenesa i Nicolasa Caussin'a.

Przypisy

Absolwenci i studenci Uniwersytetu w Lejdzie
Holenderscy teolodzy
Religioznawcy
Urodzeni w 1577
Zmarli w 1649
Ludzie urodzeni w Heidelbergu

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Wish me luck for another IV injection today for the remaining, so called, Target Therapy (Herceptin and Perjeta) at the chemo unit in my hospital. I had those treatments along with Chemo Therapy (docetaxel and carboplatin). The chemo therapy is done, but the target therapy lasts until next summer in every 3 weeks.
I started drinking a lot of liquid, hoping that a nurse will find a good vein from my arm for the treatment and (s)he does not have to do many times of "fishing" my vein.
Good luck to you today Yoko!!
A big relief when this is done at once! We did it once! Thank you, Patti!


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Messaging Grows Up: What You Can Do With WhatsApp and Its Rivals
Nathan Olivarez-Giles
@nateog
nateog
Updated Feb. 21, 2014 1:21 pm ET
If you heard the news that Facebook was paying $19 billion for WhatsApp, and didn't know what WhatsApp is, don't feel bad. While it's used by more than 450 million people, most of those people are not in the U.S. However, if you message with family and friends throughout the day, now is a great time to get to know the impressive array of messaging options provided by WhatsApp and its rivals.
You may have heard of iMessage, Facebook Messenger and Google Hangouts, but do you know KakaoTalk or Line or Viber? All of these apps are a step up from basic cellphone text messaging. In addition to sending text, photo and video, you can transmit emoticons and emoji, and you can cluster people for group chats.
These apps are available on most platforms—with the notable exception of Apple 's locked-down iMessage—so there's no excuse for avoiding friends with different mobile OSes than you. If you see a feature you like from our run-down below, check to see if the app is available in your phone's app store. Just remember, you have to get everyone else on the same app in order to make these features work.
What else might you be missing? Here's a list of advanced messaging features, and which services provide them:
Desktop messaging
Messaging on the go is great, but what about when you're stuck on your laptop at work? Plenty of apps offer an answer. Apple's iMessage allows for messaging between Macs, iPhones and iPads. Viber has both OS X and Windows apps. Google Hangouts are available through any desktop browser, plus iOS and Android devices. The same goes for Facebook's Messenger service, which also works on the Windows Phone Facebook app. KakaoTalk, popular in Asia, has a desktop app, too, though it's exclusive to Windows.

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education, any process, either formal or informal, that shapes the potential of a maturing organism. Informal education results from the constant effect of environment, and its strength in shaping values and habits can not be overestimated. Formal education is a conscious effort by human society to impart the skills and modes of thought considered essential for social functioning. Techniques of instruction often reflect the attitudes of society, i.e., authoritarian groups typically sponsor dogmatic methods, while democratic systems may emphasize freedom of thought.


Before Treatment: Paper support was separated along many of the metal "ribs" and a few sections were missing (far left).
After Treatment: Tears were repaired and strengthened with Japanese tissue and wheat starch paste. The lost support sections were recreated and the lost media was toned to integrate the image.


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Staff and Students Prepare For New Musical
PCG members dedicate hours to latest musical production.
By Calela Brooks • Nov. 17, 2016
EDMOND—More than 100 Philadelphia Church of God cast and crew members are preparing for the December 29 debut of music director Ryan Malone's newest musical, The Widow's Might, which will show at Armstrong Auditorium. Beginning with a rehearsal on November 1, the musical's chorus groups are focusing on the blocking and staging elements of the show.
Based on the book of Ruth, the project began in February, with Mr. Malone and Pastor General Gerald Flurry exploring which biblical account to portray in the Church's next musical production.
"He thought, since he was going to be getting into some deeper understanding on this book of the Bible, that it would be timely to make this the next musical," Mr. Malone said.
Since August, 15 Irish dancers from the Maguire Academy have spent 21/2 hours every week rehearsing for the six dance numbers in the show. Choreographer and instructor Paris Turgeon says the group has dedicated an estimated 30 hours to the finale alone.
Also starting in August, the crew of about a dozen pcg members began creating sets, props, lighting-design and costumes, while the main choruses rehearse weekly and bi-weekly. The musical features three main choruses: townspeople, gleaners and Boaz's servants. Outside of the two hours of rehearsal time every week, each chorus member is expected to practice on his or her own.
Before the Feast of Tabernacles in mid-October, the choruses focused on learning parts, diction and blending together, while recording engineer Ken Sarkey spent 23 hours recording the orchestra. After the orchestral accompaniment was complete, Sarkey spent another seven hours recording the three choruses, as well as small solo parts. Mr. Malone hopes to make the audio for the musical available on all major digital outlets.
After the Feast, the choruses have focused mostly on blocking, staging and choreography.
"It's a great opportunity for a group effort, with all the choirs and such," Mr. Malone said. "That makes what happens to the lead characters quite special and intimate, and it gives the audience a chance to connect to some universal emotions and circumstances in this account."
The lead roles of Naomi, Ruth and Boaz are played by Herbert W. Armstrong College voice instructor Paula Malone, sophomore Jessica Brandon and instructor Mark Jenkins, respectively.
"It's easy to look at this book of the Bible and say it's about Ruth, because of how it's been titled. But the story is just as much about Naomi, if not more," Mr. Malone said. "Boaz himself was probably widowed as well, so he ties into the main theme of the story. And that theme, or that overall message, is that God takes care of His widows. He is the might and strength of the widow. He provides what they need—whether it's in the field or in the home—whether it's financial or spiritual."
The musical debuts on December 29 at Armstrong Auditorium. It will live-stream at live.pcog.org. For more details and show times, visit ArmstrongAuditorium.org.
Undefeated–The Story of Isaiah and Hezekiah
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Theresa May's Tories break the law AGAIN – Conservative Council Chief Geoff Driver arrested for witness intimidation.
Top Tory councillor Geoff Driver, who was due to be installed as leader of Lancashire County Council on Thursday has been arrested. The Tory chief was arrested along with three other members of the Tory Party in swoops by police as part of Lancashire's long-running One Connect investigation.
The arrest came Monday morning with the Tory council leader processed by the police in Skelmersdale Police Station, then held for questioning.
The other three men arrested are Ged Fitzgerald the current Liverpool City Council chief executive, former County Hall chief executive Phil Halsall, Chief Executive of the now defunct One Connect and its sister organisation Liverpool Connect David McElhinney. The four are currently being questioned at Skelmersdale Police Station.
"FOUR MEN HAVE BEEN ARRESTED IN CONNECTION WITH AN INVESTIGATION INTO CONSPIRACY TO PERVERT THE COURSE OF JUSTICE.
THE MEN, AGED 72, 55, 58 AND 56 WERE ARRESTED AT ADDRESSES IN PRESTON AND MERSEYSIDE.
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Loans seem to be harmless contracts at first because it is just as simple as borrowing money and paying for it later. However, you have to be very keen when contracting loans most especially commercial loans because these types of loan require due diligence on your part. As much as possible, you have to pay special attention to the important things that you need to consider when doing commercial loans in order to make sure that you will never have to face any trouble or issue with your contract in the future. In order to help you contract safer commercial loans, this website will provide you with some guidelines on the important things that you need to take into consideration when doing commercial loans.
One of the most important things that you need to consider when contracting commercial loans is the interest. The interest varies in every finance corporation or any company that you will be contracting your loan with so as much as possible, you have to make sure that you are well oriented with the loan policy as well as the terms and conditions of the loan that you are going to get. This is not very hard to do because most contracts these days are provided with complete provisions on the terms and conditions that bind you in the contracts of loan that you are a part of. You cannot also be demanded of interest if it is not stipulated in your contract and provided for in writing so you must always make sure that you read thoroughly everything that is provided for your in the provisions of your contract. When you know every detail that you need to be oriented with regarding the interest of your commercial loan, you can free yourself from any trouble or unexpected liability in the future.
When you are also choosing the company that you are going to contract your commercial loan with, you must also see to it that such company is reputable enough and well trusted by many. It is important to see to it that the company you are getting is reputable enough because that is one way for you to get the best deals. In order to ensure that good reputation of the company you are going to contract your commercial loan with, you must always do your research at https://assetsamerica.com or by referring to their previous clients. For more information about commercial loans, visit this page now for more info: https://en.wikipedia.org/wiki/Commercial_mortgage.


his weekend UnDorkMommy said something to me that broke my heart.
Three days earlier I came home late as I always do on Wednesdays, just as the kids were finishing up books and snuggles before bed. We've recently been edging ever closer to finishing "Harry Potter and the Prisoner of Azkaban" (remember, you can't watch the movie unless you've read the book first). They can taste the finishline (and a new movie to watch), so they've been extra-special excited about bedtime reading lately. On Wednesdays UnDorkMommy has to handle the bedtime routine alone, and of course part of that is reading books to the big kids. We got the kids all tucked in and sat down to touch base as husband and wife. "So, how was your day teaching?" she asked.
This weekend was the local Mountain Bike Fair. We live in an outdoorsy place, so mountain bikes are kindof a big thing. It's the sort of place where parents post on facebook "Just took Jr. for his/her first time on the pump track!" (For those people out of the know, a pump track is a dirt track with mounds, and moguls and banks etc). There's a bike store near our house with some amazing pump tracks out back for all levels. We pass by the tracks whenever the family goes hiking and I've used the pump track as an incentive for the kids to learn how to ride their bikes.
Six or Seven months ago Episode IV finally got off her training wheels, and we've been working on getting her competence and confidence up to pump track levels. A few weeks ago Episode V finally got off his training wheels and we've been practicing out at the park every opportunity we get. To spur his interest and get him motivated I took him out to the Mountain Bike Fair to watch the pros go flying into the air X-games-style. I expected we'd be there about 30 minutes before his attention span puttered out and we'd be off to the next thing.
It was like walking into Disneyland for the first time. We weren't there for 5 minutes before he spotted the bunny-hill pump track just for little kids that they built specifically for this event. That was that. We walked back to the car, got his bike out of the back and three hours later we'd watched the pro aeronautics, gone on the kids' pump track (twice), ridden a real off-road trail, checked out all the vendors, sat on a hay bale eating pizza and popsicles watching a racing event, and acquired some impressive sunburns. In short, it was amazing! He even got a medal. Episode V and I came home totally pumped (no pun intended), totally exhausted and totally overstimulated.
We spent the second half of Saturday at the park with the whole family. The two big kids practiced off-roading on their bikes with me coaching and cheering them on, and UnDorkMommy spent most of her energy keeping Episode VI from eating sand and getting run over by his older siblings. By the end of the day everyone was exhausted, and all three kids went to bed relatively easily. After Episode IV was asleep, my wife came down the hall and walked up behind me as I was checking my Email. She put her hand on my shoulder. I could tell something was weighing on her heart. That's when she said it.
I had absolutely no idea what to say.
And I used to respond with, "Yep. But someday our kids are really going to appreciate it." It would seem that perhaps that prophecy has come true.
Sorry, kids. This is your daddy.
Let's be clear, my wife is the most important, most amazing, most crucial element of this entire family. When I'm off figuring out how to get an arcade game into my house, she's the one making sure the kids are having a healthy lunch. When I'm spending my time writing blog posts, she's the one arranging their extracurricular schedules. She's the one who makes sure they have a sweater when they leave the house. She's the one who makes the sandwiches for their lunch just the way they like 'em. She's the one who plans and makes dinners every night. She's the one who gets them on time to doctor's appointments, and swim lessons, and play dates. She's the one who makes sure the milk in the fridge isn't sour. She's the one who makes sure their bedsheets are clean, that they take their medicine and that they play nicely with one another.
She's the last person the kids want to see before they go to sleep. She's the first person they want to see when they wake up. If they have a bad dream in the middle of the night, it's her body they need to feel next to theirs that makes the monsters go away (and all that stuff goes for me as well).
Sure, I'm the one who does the epic lego marathons. I'm the one who knows all the words to all the Disney songs. I'm the one who does the lightsaber fights and dances to "Gungnam Style" in the livingroom. But when there's a scrape on the knee, it's her kisses that have the healing magic. On a rainy day it's the cookies she makes that turn everything around. When someone is sick, it's her arms they crawl into for comfort. She is the rock-center, the core, the heart of our family. She nourished those children in her belly. She birthed them. She nursed them as infants from her own body. She dedicates every waking moment to nurturing them as children and to helping them grow into compassionate, confident, amazing human beings.
The truth is all this dorkiness, all this childlike buffoonery… it's all for show.
I'm a dancing bear at the circus making a fool of myself in front of my children because — That's. All. I've. Got.
It's a desperate act to be relevent in the lives of my kids because ultimately the short-lived sugar rush of dessert isn't what sustains you the way Mommy's healthy meal does. It isn't what keeps you alive. Sure, I have my role to play in nurturing our children. Sure, their lives are enriched because I'm demostrative, I'm involved in their lives and I'm totally invested in the family. Yes, their lives are immeasurably better because I love them so much.
But compared to the absolutely crucial, nourishing, healthy, dependable, selfless love that they get from their mother — the nourishment that none of us in this family, myself included, could live without — I have to put on the superhero T-shirts. I have to build the zip-lines in the backyard. I have to make the Transformer Halloween costumes from scratch. I have to do the voices when I read Harry Potter.
Because in all honesty, compared to my wife, I just can't compete.


TAMPA, Fla. -- Victor Hedman scored twice and Ben Bishop stopped 28 shots Sunday, helping the Tampa Bay Lightning beat the New York Islanders 4-0 and reach the Eastern Conference final for the second straight year.
Tampa Bay eliminated the Islanders in five games, winning four straight after dropping the opener of the second-round series.
Hedman scored an unassisted goal from the slot at 13:49 of the first period, then beat Islanders goaltender Thomas Greiss again on a second-period power play that gave Tampa Bay a three-goal lead.
Nikita Kucherov and Brian Boyle also scored for the Lightning, who will face either the Pittsburgh Penguins or Washington Capitals in the East final. The Penguins lead the Capitals 3-2 and Game 6 is Tuesday night in Pittsburgh.


Presider: Bishop Cantú. The Mass will be followed by "Comida" at St. Jude Center. Music will be available for your enjoyment. Plan to spend the day with Friends and Family! Location: Highway 70 East, Mile Marker 281, San Patricio, New Mexico.


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How Textron's Larry La Sala Is Corralling the Conglomerate
Textron tasks its legal team with cycling between a number of different industries. VP and deputy general counsel of litigation Larry La Sala explains how he handles it.
By	Randall Colburn
Larry La Sala, V.P. & Deputy General Counsel – Litigation, Textron
"I've been drinking out of a fire hose," Larry La Sala jokes, reflecting on the chaos that's been pouring across his desk since he became vice president and deputy general counsel of litigation at Textron, in July 2017. But, having been with the company for sixteen years, La Sala knows what he signed up for; Textron, which has become an industrial conglomerate in the fields of aviation, defense, security, and more since its founding in the early 1900s, encompasses multitudes.
His external partners have been impressed with his approach to the variety of work. "I am so proud to work with Larry, and I know his in-house team at Textron feels the same," says Neil A. Goldberg, a partner at Goldberg Segalla. "He is inspiring to be around. His sophisticated, forward-thinking approach to complex problems, coupled with his broad experience, helps assure a highly motivated, efficient, and effective legal department."
La Sala estimates that Textron has acquired roughly three hundred different companies since 1950. In his current position, La Sala oversees a staff of five full-time lawyers, each of whom specializes in a particular area of Textron's portfolio. He and his team work with the legal departments of Textron's numerous businesses, and here he breaks down how they multitask between them.
What do you mean when you say you're "drinking from a fire hose"?
There was an interesting combination of circumstances when I took over this job. My predecessor was promoted to an executive vice president position outside the legal department, so she was busy transitioning into her new role. I also inherited the cases she was working on, on top of my own—and had a senior lawyer on my staff in the process of retiring. And a few months before I started, we purchased Arctic Cat, and that was a whole new area of litigation we had to integrate into the portfolio. I've had a lot to get up to speed on.
How are you managing all that on top of such a diverse portfolio?
One of the things that has helped me tremendously in the last eight to ten months in this job is having worked over the years with almost all of Textron's businesses on nearly every type of litigation. So, while I certainly needed to understand a greater depth of detail about some businesses, I was not a complete stranger to anything that we did in the litigation function. That was helpful.
It must also help to have a staff that has specific specialties.
Given the breadth of the company, the amount of different industries we're in, and the different types of litigation, I don't think anybody would be able to do the job without having some good people that you trust. Having spent ten years at Gibson, Dunn & Crutcher, it was very comforting for me to come to a place where they had such bright, dedicated lawyers. I mean, it's not uncommon for our lawyers to be here ten, fifteen, twenty years or more, and that sort of continuity is really helpful, particularly when you have a company that's in the business of buying and selling companies.
So, our litigation staff in the corporate office and at our businesses is all folks who have had a significant career in outside law firms. They come to us as trial lawyers, knowing how to manage and try cases. We have in-house people who are specialists in these areas, whether it be in aviation regulations or consumer products.
Do you ever allow your lawyers to operate outside of their specialties?
Candidly, my primary goal is to get people, to the extent I can, out of their containers. I want to get them as wide a breadth of experience as I can and, in some instances, even take them out of their comfort zone. You don't stay and work here unless you have some desire for diversity.
But, I also offer a lot of autonomy. I'm working with professionals with substantial track records, and I want to give them all the assistance they need while also letting them do their jobs the way they know how. In many cases, they have more experience than I do in their particular specialty.
Is it difficult keeping everyone on the same page sometimes?
Well, to do that, you need processes in place where you have lots of communication and integration between the corporate-office litigators and the business-unit litigators. Certainly in my position now, overseeing all of those lawyers, it's on me to make sure that the communication process is in place and everyone from the lawyers to the finance people to the business people are on the same page.
How would you say you've had an impact on the actual business in your role?
Well, more than ten years ago, I helped to build our own in-house e-discovery program in the litigation group so that most of the work that would get farmed out to vendors in terms of collecting and processing information we could do in-house. And, depending on the year, we were tracking probably $2–3 million or more in savings, and that's real savings.
We also have very high success rates in terms of managing cases, particularly repetitive types of litigation like toxic tort. We have programs in place that really help us handle those cases in a very efficient way. Most of the time we're on the defense side, and so, for us, resolving litigation without it having a material impact on the company is really critical.
What would you say is the most satisfying aspect of your position?
Honestly, I think the most satisfying part for me, which I didn't anticipate coming here, is having grown into being as good a businessperson as a lawyer, bringing those two worlds together. Sometimes, the business solution to a case is not identical to the litigation solution to a case. So, for me, when I can bring those worlds together and the CFO or finance director is happy with the resolution of a case, that's deeply satisfying.
Photo by Julie Campanini
Expertise Spotlight
Textron partner Goldberg Segalla is one of the largest and fastest-growing law firms headquartered in the US. With more than 350 attorneys and more than twenty offices in New York, Chicago, Los Angeles, Philadelphia, Miami, St. Louis, and other major business and economic centers across ten states, the firm advises and represents clients from a wide range of industries in complex matters across the US and around the globe.
The firm defends high-exposure product-liability and mass-tort claims, represents companies in toxic tort and environmental matters, handles complex commercial and insurance-coverage litigation, guides clients through multijurisdictional transactions, and advocates for clients in all forums of alternative dispute resolution. Its lawyers draw on this extensive collective experience to provide proactive legal and regulatory counsel that helps clients minimize and manage risk.
Goldberg Segalla's collaborative culture and team-first philosophy have earned it respect and admiration from peers and clients, a spot on Fortune's national Best Workplaces list, and continual placement in statewide and regional rankings of the best places to work. The firm values and rewards efficiency and collaboration in all its people, which ultimately drives a superior law firm experience for its clients.
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Resolve behavioral changes in your converted code to replicate the original source code in this software.
Before you can resolve behavioral changes in the new source code, you must convert code from a supported version of LabVIEW for use with LabVIEW NXG. Refer to Converting Your Code for help converting code for use with LabVIEW NXG.
If the new project did not launch automatically after the Code Conversion Utility finished converting your source code, launch the newly generated projects using LabVIEW NXG to begin reviewing the converted code.
In the Conversion Report tab, review the messages and determine if you need to resolve any messages by updating the original source code.
Conversion messages that list SourceFile in the Category column usually correspond to issues that can be resolved only in the original source code.
If you make any changes to the original LabVIEW source files, convert the original source files again. Because the Code Conversion Utility generates a unique copy of the converted code each time it runs, the code generated when you rerun conversion will not include any changes you made to code from a previous conversion. This means you should always resolve issues by updating the original source files before modifying the converted code.
After resolving the issues in the original LabVIEW source code and rerunning conversion, identify messages that affect the core functionality of your code and begin resolving changes in your converted code by evaluating the severity and category of the messages.
NotConverted The Code Conversion Utility could not access a missing file, file in vi.lib, password protected file, or unlicensed file.
If a core feature of your code is not supported in this application, wrap the code in a subVI in the original source code, and call the subVI into this application using a VI Interop node. Instead of using many VI Interop nodes to replace individual missing nodes, attempt to modularize calls to the previous LabVIEW product into as few VI Interop nodes as possible. Each time you call code outside of this application, the efficiency of your code decreases.


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⬅ How to Engage Students and Find Your...
Passion Projects in Kindergarten and... ➡
7 Strategies I Use When Students Make Apps (or Do Any Genius Projects)
Vicki Davis on episode 307 of the 10-Minute Teacher Podcast
I'm so excited! This is the time of year we are making apps. Now, while I'm talking about making apps in today's show, this will actually apply to passion projects, to making movies, any type of long-term project where you have the students brainstorm and create.
SMART's Give Greatness contest is today's sponsor. SMART wants to recognize educators across the globe who inspire greatness in their students, peers or community. Nominate your favorite educator at coolcatteacher.com/greatness.
Each nominee and nominator will be entered to win a classroom technology package. The winning nominator and his or her nominee each win a $20,000 package including one 7000 series SMART Board and SMART Document Camera, 30 Chromebooks, and SMART training and implementation. Enter a great teacher today.
Because these seven principles that I'm going to give you apply to any type of project, where you have kids ideate, create projects, and work together in teams.
Listen to this Blog Post
Now I do want to give a shoutout to my friends at MAD-learn. We used their app platform — and no, they did not pay me to say that — I just love their platform, and that's what we used to make our apps.
So the first thing is idea generation. It's also called ideation.
Strategy 1: Idea Generation, AKA Ideation
This is really the most important part, because it's setting you up for whether you're going to succeed or not in your project.
If you're going to have team problems, this is when you're going to see them. You really have to observe the groups and make sure they're working well together.
You also want to push kids to do things that they're passionate about doing.
For example, in this app project that I'm working on now, I had one group of kids that was going to make a Dog Dictionary, about all of the different types of dogs that were out there and that sort of thing.
I wasn't entirely happy with it, but I never usually say, "No," directly, unless it's going to endanger somebody or something like that.
I do a red light – yellow light – green light process which means, "Well, you're about get the red light if you keep doing that." Or I'll say, "Right now, you're in yellow light, but this is what you need to do to get to green light." Green light obviously means that you're going ahead into production.
This is a term even used in Hollywood from what I understand, although I've never been really involved in movie making in that way.
So they need to have lots of ideas. They need to connect. I try not to intervene.
For example, I have a boy who came and said, "Ms. Vicki, I want you to red light my group. I don't think it's going to work, and I don't want them mad at me."
And I'm like, "OK, why can't you just have this conversation with them?"
"Well, I just want you to handle it for me."
And I said, "Well…" and we talked about it for 10-15 minutes, and he said, "Well, you're not going to intervene."
And I said, "No, here's the thing. I'm not just teaching about apps here. We're actually teaching about how to collaborate, how to work together. And part of life is having difficult conversations with folks. And I do agree with you, but I'm not entirely sure that me red lighting it is the right thing to do."
Certainly, there is a time for me to be the bad guy, but this wasn't one, because this particular student is very gifted, but also needs to learn to work with others. So I did not red light it, and they were moving ahead. Dog Dictionary was going to be it.
And I turn around, and this young man had a conversation with his team that he thought, "Well, you know what? This is probably not going to make it, and I think that there are other apps out there that are too much like this. Maybe we should go to other teams that might be more successful."
Well, all of them decided to red light their own app, and they split into three different teams. Now, this was the perfect outcome, but it was a perfect outcome because THEY decided it. They made the decision, and it was what they wanted to do.
I felt great about it.
So idea generation is so important. You want to come up with lots of ideas, you want to push them, help them do that.
So then the second thing is I like students to go in after they've kind of come up with their idea. I create a template or a hyperdoc in Google Doc. They'll turn around and make a copy of that, and it has everything they need to fill in.
Complete the Google Doc
Now I have constraints here, so for example, they have to start with a 50-word description of their app. They have to keep it to 50 words because if they were going to have their app in the App Store, that's pretty much how many words it would be.
And I want them to make it compelling, and about why we need this app. And they have to collaborate.
So I'm actually looking at the revision history. So I see which kids are coming into class, I'll pull up the four or five Google Docs for all those kids. I'll go through them and look at the revision history, and I'll say, "Hey, I only see one person editing on your Doc today. What's going on?"
And then we have the conversation. You should see their eyebrows come up when they realize that they're not collaborating. Part of the requirement to get a green light is that they have to have a good working collaborative team. Because if you don't have a collaborative team, you're not going to have a good project.
Now the important thing is to realize that these projects are bigger than one person can do by themselves, and this is why I love having massive projects that are too big for one student to do by themselves.
You want students to work in teams. No one person can run a Fortune 500 company by themselves, and we want kids to know how to work in groups like this. We sketch things out.
Also in this document, have them do research before they can create their app and get the green light. They've got to prove to me that this app is needed, that they've done their research. They've got their out to hyperlink to that.
I actually require every single student to put in three items of research in the document. Well, I could do this collaboratively, but if I have every student having to research, I make sure that all the students know how to hyperlink but also that they can effectively research and they know how to do that as well.
So this is when I kind of giving them a test. I have five big pieces. It takes 2-3 days. They're not going to get the green light unless they move through this document and unless I see that they're working effectively together.
Now in this document, they also have to come up with fifty ideas for their app names! Well, you could think, "Oh my goodness, why would you do that?"
Well, I have found the best app names typically come somewhere between number seven and number twenty-one-ish. Kids are so worried about looking cool that you have to push them past the cool factor, because honestly, if you're afraid of looking uncool, you're afraid of coming up with good ideas.
A lot of times what will happen is, the kids run out of ideas, and finally, the cool thing becomes just throwing out ideas. They'll laugh, and they'll have dumb ideas. Right in the middle will be some incredible ideas. You want to teach kids how to brainstorm. You have to accept all the ideas, throw them into the document, and then decide what's the best.
We had a long conversation about what makes a great app name. We have to discuss SEO (Search Engine Optimization) and having a name that can be found on the App Store. Also, alliteration! We like things — like Dog Dictionary — that have the same first initial.
We also like things that rhyme. We have this one app called the "Swole Patrol" and that's an app that's about exercises by teens for teens. That's a great one. They had another name that was just not so good.
So again, don't look for these on the App Store yet, because they're not there. They're just ideas that the kids are working on. But that's kind of what we do.
Now, the third piece of this is that you want kids to have jobs. So we have PMs (Project Managers), APMs (Assistant Project Managers), and then Graphic Designers. Sometimes we'll have Marketers doing something with social media. We'll usually have an Editor. This is important because in apps, you want to give credit.
#2: Assign roles
But the thing that I always tell the students is that you may get the title, but to keep it, you have to earn it. So they can give each other all the titles they want. And sometimes they'll propose titles, and they'll say, "OK, I want this person to do the app trailer."
OK, I'm fine with that. Thye can be the director of the app trailer, but if somebody steps in and does their job for them, they will lose that title. In the real world, you have to do the job.
They are able to list these on their transcript for the school, so it's kind of awesome for the kids to say, "I was the PM or the APM of a particular job." And they learn so much when they have that.
And it's also easier for me, because you know, at the beginning of class, I'll say, "I need to meet with all the PMs and APMs at my desk."
I'll kind of just tell them where everybody needs to be, and then they'll go out and handle their teams. I'll just turn around and I'm kind of like the CEO or the head coach, just trying to coach all these teams to move forward. I really want them to be leaders in their own groups.
#3 Stages of App Development
Now, there are also phases of development. So, as I said, there's the red light, the yellow light, and the green light.
Red light means we have stopped production. Typically, the kids will red light themselves. It is very rare that I have to red light them.
Yellow light means that you can proceed, but you have to fix this, this, and this before you get a green light.
And the green light means you can go ahead to the next stage of production.
Well, the first stage is to get past the Google Doc, and then you have to get past me, and then I give you a green light. Then you go into App Development.
So then they'll go in and they'll do their site map, and they're also going to get their basic theme, layout, and that sort of thing in the MAD-learn platform, to kind of show what the app will look like and do basic development.
#4: Presentation for an Authentic Audience
Then, they have to make a foam board with their graphics and they go in front of the principal and the curriculum director and typically another teacher. They're having to present. They're having to sell their app. They're also having to show the app design and convince those that they can move forward.
At this point, I will usually have a limited number that can move forward. They'll have to meet certain criteria. Think of it like a drivers test. You're in the state of Georgia, and you have to make a 75% to pass your drivers test. That number seems a little low to me, but there you go. So I'll have a rubric, and you have to make a certain number of points on those rubrics to get the green light to go ahead to Phase Two.
That's typically how I do it, which means about 25% of the apps are probably going to drop out of the competition just because they don't have enough points to be able to be green-lighted to the next phase.
Then, the last phase is we actually have, in front of the whole school and a judging panel, to determine which app is going to go on the App Store. And you could say, "Well, why do you want to do that?"
#5: Competing for Limited Resources
Well, that's my fifth point. It's OK to compete for limited resources. Sometimes when you have a movie, or when you have an app, or when you have just about anything that you produce that costs money… It costs money, and you have a limited amount of money.
So we have enough money, pretty much, to put one app on the store. Somebody in the audience might decide to fund another app. That's happened before. But at this time, typically, it's just one app.
So they're competing to see which one is the best app and which one's going to go live on the App Store. And it's perfectly OK to do that. That is the real world, and that is how it goes.
We've had quite a few apps. One's called iCare, DroneZone, one's called unCut. There's a lot of apps, and you can look at the MadStore, which is kind of like a staging area for apps before they go live on the official Apple Store or the Google Play Store, those places. You can see a lot of student apps in there in the staging area of the MAD-store.
#6: Copyright
So the sixth thing is copyright. Now, this is one of the hardest things. The kids who wanted to do the dog app that we talked about earlier. I really think that they thought it would be pretty easy because they could just copy and paste information.
You can't do that when you're making an app. You can't just take music when you're making a movie! Kids just think that they can just take whatever they want, and that's not the way the world works.
We've really got keep a handle on that copyright. What I typically do is… I will pull up the platform and copy-paste some pieces of it into Grammarly, and I have Grammarly Pro, which will do a Plagiarism Check. It will tell me pretty quickly if we have a plagiarism problem. Then they could end up with a red light.
Now you could ask, "What happens if somebody ends up in a red light?"
Well, we have the drafts — so if you can think of the NFL draft — we sit down and we figure out those who don't have a team. The Project Managers that are left will just kind of draft those folks.
Now sometimes, there are behind the scenes negotiations that go on.
People notice there's somebody who's really great at graphic design on the other team, and they'll want them on theirs. There may be some conversations, some trading. There are things that happen behind the scenes. But everybody ends up with a team, to work on a team in the final competition.
So you have app teams getting larger and larger, getting more and more done. Everybody has to create a certain number of pages. You can end up with an app with a good 30-40 screens which is a well-developed, very strong app by the end.
The draft is interesting. I always tell students, "If your team got red-lighted, would you want to be the last one drafted?"
Now they'll never know because the draft happens with PMs and APMs, privately in my room with the door closed. But the draft is actually very exciting, and it teaches kids so much about the kind of folks that people want on their team. They want people that are easy to work with. They want people who pull their weight. They want people who will bring something to the team.
It's just a fantastic experience to do that.
And then the last piece of this is number seven. Students need to develop collateral materials that go with whatever their project is.
#7: Development of Collateral Materials
So while students are creating apps, I have them create a website. They'll have an app trailer. They'll typically create a Twitter, Instagram, social media type platforms to go with it. So that it's a full offering. It's a full product they've really thought through. Those are really parts of what they show to the final Shark Tank competition, they'll have their app trailer at that point.
For Phase Two, they won't have their app trailer. You have to get a green light for Phase Two to get to where you're going to have an app trailer.
So they have all these collateral materials, and it's a really a very well-developed project. Everybody has a team. Everybody is on a team. They can have those conversations.
For my students, I have found, that when they go to college and when everything else is equal. You and all of the other folks who are interviewing for that scholarship have the same GPA, and you have the same activities. You're the best of the best.
When my students can kick back and talk about the app that they made, and that they were the Project Manager in the Shark Tank Competition, and how they spoke and how they were able to work through the problems that you have in teams, how you were able to motivate people who maybe aren't very motivated because it's the end of the school year… THAT really does make a difference.
I find that it's also very engaging for students and very fulfilling to have a meaningful product that comes out of this whole process.
So I've given you seven strategies, seven techniques that I use when we're making apps.
I hope this has been a helpful Ed Tech Tool Tuesday, and kind of gives you an overview of how I like to run things.
This is a typical project setup for me. The students are running it. I'm the coach. I'm helping the kids. I'm encouraging the kids. That sort of thing. So I hope this gives you some insight.
Feel free to tweet me @coolcatteacher if you have questions about this. Also take a look at MAD-learn and their really cool books! Thanks!
Contact us about the show: https://www.coolcatteacher.com/contact/
Transcribed by Kymberli Mulford [email protected]
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