## Tagged Questions

1answer
199 views

### Fibered knot with periodic homological monodromy

It is well-known that there exist pseudo-Anosov automorphisms of surfaces that act trivially on the homology: they form the Torelli group. Similarly there exists pseudo-Anosov auto …
0answers
191 views

### lifts of maps to $\mathcal{M}_{1,1}$

Hi, here's there's a construction about elliptic curves that I do not completely understand. Suppose I consider the two following families of elliptic curves over $\mathbb{C}^*$. …
2answers
150 views

### Genus one fibered links

It is well-known that the only genus one fibered knots are the trefoil and the figure-eight. On the other hand, there exist infinitely many fibered links for any fixed higher genus …
1answer
112 views

### An analog of Picard-Lefschetz theory for finite coverings in lieu of embeddings

Suppose that $f\colon X\to \mathbb P^N$ is a finite morphism, where $X$ is a smooth projective variety over $\mathbb C$. Then one may consider monodromy of the (singular) cohomolog …
1answer
205 views

### weight monodromy conjecture for curves?

Hi, Is there a simple proof of the weight monodromy conjecture in the case of a curve over a mixed characteristic local field? Thanks!
0answers
284 views

### Grothendieck monodromy theorem for l-adic sheaves

Hi, Suppose that $F$ is a local field, $G_F$ its Galois group, $I$ the inertia subgroup, $k$ its residue field. Let $X$ be a finite type scheme over $k$. Let $C$ be a constructibl …
3answers
460 views

### Monodromy group of 1-dimensional families of hyperelliptic curves

If $f: \mathcal{C} \rightarrow \mathcal{P}_{2g+2}$ is a general family of hyperelliptic curves (defined over $\mathbb{C}$), we know that the algebraic connected monodromy group \$M …
0answers
378 views

### Rigid Uniformization vs Grothendieck’s Local Monodromy Theory

I've noticed that some interesting results about abelian varieties can each be proven using one of two ways: the theory of rigid uniformization of abelian varieties or Grothendieck …
1answer
294 views

### Quasi-unipotent monodromy for general families

This must be a naive question, but I'm wondering about the definition of the quasi-unipotent monodromy for general (not only 1-parameter families). The problem is that usually in t …
3answers
450 views

### Relationship between monodromy representations and isomorphism of flat vector bundles

This question is somehow related to this one. Let $M$ be a smooth (compact, if you wish) connected manifold. Then, it is well known that there is an equivalence between the isom …
1answer
263 views

### What is the mod l monodromy of a generic trigonal curve?

For a hyperelliptic curve H, the mod 2 monodromy is smaller than $GSp_{2g}(F_2)$ -- since the two torsion of the Jacobian H is generated by differences of Weierstrass point, the mo …
0answers
122 views

### Irreducibility of monodromy of eigenspaces of families of cyclic coverings

In the article "La conjecture de Weil", Deligne proves that for the primitive cohomology of a universal family $f:X \rightarrow S$ for $M_{d,n}$ the moduli stack of hypersurfaces o …
2answers
249 views

### Analogue of Shafarevich-Ogg’s theorem over complex numbers

Let $f:E\to D^*$ be a family of complex elliptic curves parametrized by the punctured open disk $D^*.$ Assume that the monodromy on $H^1$ is trivial (i.e. $R^1f_*\mathbb Z$ is a co …
1answer
602 views

### Monodromy groups of families of abelian varieties: a reference request

In Serre's letter to Vigneras of 2 Oct 1986, he summarizes a course he's giving in Paris, explaining how to control the image of the mod-l Galois representations attached to abelia …
1answer
448 views

### monodromy and global cohomology

Let $C$ be a compact Riemann surface, and let $U$ be a Zariski open subset in $C.$ Let $L$ be a local system (with coefficients $\mathbb C$ or $\mathbb Q_{\ell}$) on $U.$ For each …

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