All Questions
Tagged with perverse-sheaves hodge-theory
10 questions
3
votes
0
answers
147
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Tate conjecture for singular varieties in terms of intersection homology
In his book “Mixed motives and algebraic K-theory”, Jannsen generalizes the Tate conjecture to a potentially singular projective variety $X$ over a finitely generated field. The statement is the same ...
- 658
5
votes
2
answers
651
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Hodge theoretic properties of intersection cohomology
Let $X$ be a complex projective irreducible reduced variety. It is well known that the intersection cohomology of $X$ satisfies versions of Poincare duality and hard Lefschetz theorem.
Does it admit a ...
- 241
4
votes
0
answers
114
views
Simpson correspondence for perverse sheaves
Let $X$ be a projective complex manifold. Then Simpson's correspondence from nonabelian Hodge theory shows that the category of semisimple local systems on $X$ is equivalent to the category of ...
- 615
2
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0
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94
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Hard Lefschetz for perverse sheaves on Kähler manifolds
Let $(X,\omega)$ be a compact Kähler manifold, $k\ge0$, $P\in Perv(X)$ be a semisimple object, then do we have the hard Lefschetz isomorphism between perverse cohomology sheaves $\omega^k:{}^p\mathcal{...
- 615
3
votes
0
answers
240
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What sorts of weights for perverse sheaves were or can be computed?
I am studying certain weights for (triangulated categories of relative) motives. Those are interesting; yet one can hardly say that they are very much explicit or effectively computable. So, I would ...
- 16.9k
4
votes
1
answer
437
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Smooth mixed hodge modules - representations of fundamental group?
I do not know much about mixed Hodge modules. I would like to ask: Let $X$ be a smooth connected algebraic complex variety, with a chosen point. Could one describe smooth mixed Hodge modules on $X$ as ...
- 40.2k
4
votes
0
answers
290
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The associated graded of a mixed Hodge module
Unfortunately this question will be a bit vague, since the question revolves around a memory of something I may have heard in a talk (long time ago).
Let $X$ be a smooth complex variety. Let $MHM(X)$ ...
- 1,595
3
votes
1
answer
667
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Polarizable variations of (mixed) Hodge structures
I am trying to come to grips with Saito's theory of mixed Hodge modules (slightly) beyond just the basic axiomatic formalism. I will take my Hodge structures and sheaves to be rational, but I would be ...
- 35.2k
5
votes
0
answers
281
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Mixed structures on Hom spaces induced by mixed sheaves
Let $D^b_m(X)$ (resp $D^b(X)$) denote the derived category of mixed Hodge modules (resp. constructible sheaves) on a complex variety $X$. Let
$rat\colon D^b_m(X)\to D^b(X)$
be the `forgetful' ...
- 1,595
23
votes
2
answers
5k
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What exactly does the weight filtration in Hodge theory have to do with the Weil conjectures?
Let $X$ be a variety over $\mathbb{C}$, say separated. According to Deligne's results, there is a "mixed Hodge structure" on the total cohomology $H^\bullet(X(\mathbb{C}), \mathbb{Z})$. One component ...
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