Early on in “The Killing,” the American adaptation of a Danish thriller that has had a talked-about run on AMC, an unusually creepy funeral director guides a pair of bereaved parents through the retail dimensions of his mortuary. Mitch and Stan Larsen have lost their 17-year-old daughter, Rosie, to a deranged act of violence and stare achingly into the bottom of an expensive coffin they cannot afford. Trailing the couple as though they were shopping for hatchbacks, the undertaker offers that the object of their attention is “a beautiful choice for a young girl.” He goes on to instruct the Larsens on how their child should look for her interment, discreetly relishing the thought of her corpse in a pretty dress.  âThe Killingâ on AMC concluded the finale of its premiere season on Sunday.  The latest on the arts, coverage of live events, critical reviews, multimedia extravaganzas and much more. Join the discussion.  Even in the context of a series committed to brutally haunting imagery, the scene manages to leave an exceptional chill, not for the obvious suggestion that death can amount merely to another consumer experience, but for the idea that something beyond detachment — perversion in fact — is required to remain inured to the horrors of loss.  “The Killing,” which concluded its first season on Sunday night with the tenuous resolution of the central crime, Rosie’s murder, has been as much mystery as melodrama. That might seem like an odd description for a project that has so consistently and beautifully resisted transparent emotionalism. With its lyrical pacing, restrained performances and a palette so visually cool that it feels as though you are watching from inside a Sub-Zero, “The Killing” is at once a procedural and a rich exploration of the perils of obsession. In this instance the obsession is death, and in the show’s overarching ideology its impact is unfailingly totalizing and destructive.  The dangerously self-contained hero, Detective Sarah Linden (Mireille Enos), immerses herself so deeply in her casework, identifying so thoroughly with victims, that the men in her life uniformly disappear: first her child’s father; then a fiancé and briefly her teenage son, who is left to fend for himself in a motel room most days as his mother routinely loses track of the hours, her head buried in the forensics of the most gruesome mortalities.  Initially the series was advertised with the tag line “Who Killed Rosie Larsen?,” a question it answers by the penultimate episode. (Read no further if you haven’t made it there.) The murderer is, on the face of things, a patrician do-gooder, a Seattle city councilman running for mayor. But grief over his wife’s death long ago, presumably, has driven him to all kinds of baroque depravities. The Larsen story line, in its original iteration in “Forbrydelsen” on Danish television, spanned 20 episodes. The American version lasted only 13, and the primary casualty of truncation is an insufficient look at the psychologies of murderer and victim.  How Councilman Darren Richmond (Billy Campbell), of Connecticut and Dartmouth, became the kind of widower for whom scotch was an inadequate solace, is left entirely to speculation. Instead we are asked to buy wholesale the notion that as Richmond maintained an impeccable public image, he was threatening (and ultimately drowning) young prostitutes who vaguely resembled his wife. Politicians manage secret lives all the time, as the news and “The Good Wife” remind us. But it is fair to say that it is one thing to be concealing a mistress in Argentina and it is quite another to be running a campaign while simultaneously conducting an alternative life as Jack the Ripper.  (As a matter of due process it should be said that the series satisfies conspiracy theorists with the .0009 percent chance that Richmond is actually not guilty. The sane among us will run, as they say, with the facts on the ground.)  Among the show’s other preoccupations has been the notion that motherhood is rarely immune to delusion. (“The Killing” is at once a closed book and a work in progress. When it returns for a second season, it will focus on a new case and, presumably, a new set of concerns.) Sarah Linden refuses to accept that her inattentiveness is gravely affecting her son until she is forced to reckon with her absence around him. And in Mitch Larsen (Michelle Forbes) we bear witness to a character who is present in her daughter’s life and yet still positioned at a significant remove from the darkest secrets of her adolescence. In the end, of course, this is the scariest aspect of all.
In the season finale of âThe Killingâ on AMC, the murder of Rosie Larsen is resolved, but with a touch of uncertainty.