Perverse coherent sheaves

By D. Arinkin, R. Bezrukavnikov. 2009

117 citations recorded by the source corpus.

We describe an analogue of the notion of a perverse sheaf in the setting of the derived category of coherent sheaves on an algebraic stack. Under strong additional assumptions the construction of coherent "intersection cohomology" complexes works. This paper supersedes the preprint arXiv:math/0005152 by the second author.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c32f3fc9793a78764f09ccd4de921a2b1013cffe

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On exact $\infty$-categories and the Theorem of the Heart (2012, methodology): “heory of X. Let us list two special cases of this. (7.1.1) Suppose S a set of prime numbers. Let ES be the full subcategory of Db(Coh(Z)) generated under extensions by the objects Z, {Z/p| p∈ S}, {Z/p[1] | p/∈ S}. Then ESis an abelian categorywhose K-theory coincides with the K-theory of Z. 22 CLARK”
Holonomic D-modules on abelian varieties (2013, unknown): “Popa [Pop12] noticed that such codimension bounds can be expressed in terms of a certain nonstandard t-structure on the derived category, introduced by Kashiwara [Kas04] and Arinkin and Bezrukavnikov [AB10] in their work on “perverse coherent sheaves”. In our context, codimension bounds and t-struct”
Derived Categories (2016, background): “In algebraic geometry one can also consider perverse coherent sheaves; see [187] and [4].”
GENERIC VANISHING THEORY VIA MIXED HODGE MODULES (2011, methodology): “We use this observation to produce natural classes of perverse coherent sheaves [2, 15] on the dual abelian variety Â, and on the parameter space for Higgs line bundles Â× H0(A,Ω1 A).”
Autoduality of compactified Jacobians for curves with plane singularities (2010, background): “The proof is naturally given in the language of perverse coherent sheaves ([6]).”
On two geometric realizations of an affine Hecke algebra (2012, background): “11], while (b) follows from part (a) by comparing it with the definition of the perverse coherent t-structure in [4].”