相关论文: Notes on Beilinson's "How to glue perverse sheaves…

We generalize the decomposition theorem for perverse sheaves to Artin stacks with affine stabilizers over finite fields.

We briefly introduce the theory of perverse sheaves with special attention to the topological situation where strata can have odd dimension. This is part of a project to use perverse sheaves on the topological reductive Borel-Serre…

We provide a generalization of the Deligne sheaf construction of intersection homology theory, and a corresponding generalization of Poincar\'e duality on pseudomanifolds, such that the Goresky-MacPherson, Goresky-Siegel, and…

Bezrukavnikov (later together with Arinkin) recovered the work of Deligne defining perverse $t$-structures for the derived category of coherent sheaves on a projective variety. In this text we prove that these $t$-structures can be obtained…

Let G be a reductive algebraic group, with nilpotent cone N and flag variety G/B. We construct an exact functor from perverse sheaves on N to locally constant sheaves on G/B, and we use it to study Ext-groups of simple perverse sheaves on N…

In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves…

Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if…

In two articles by Barthel, Brasselet, Fieseler and Kaup, and, Bressler and Lunts, a combinatorial theory of intersection cohomology and perverse sheaves has been developed on fans. In the first one, one tried to present everything on an…

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…

Let $X$ be a topologically stratified space, $p$ be any perversity on $X$, and $k$ be a field. We show that the category of $p$-perverse sheaves on $X$, constructible with respect to the stratification and with coefficients in $k$, is…

Using techniques of [BKV], we construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the regular-semisimple bounded locus of the loop group LG and prove that the derived $\tau$-coinvariants of affine…

The higher direct image complex of a coherent sheaf (or finite complex of coherent sheaves) under a projective morphism is a fundamental construction that can be defined via a Cech complex or an injective resolution, both inherently…

This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and…

The purpose of these lectures is to introduce the notion of a Stokes-perverse sheaf as a receptacle for the Riemann-Hilbert correspondence for holonomic D-modules. They develop the original idea of P. Deligne in dimension one, and make it…

An intrinsic construction of the tensor category of finite dimensional representations of the Langlands dual group of G in terms of a tensor category of perverse sheaves on the loop group, LG, is given. The construction is applied to the…

We study the categories $\mathrm{Perv}_{\mathrm{thin}}$ and $\mathrm{Perv}_{\mathrm{thick}}$ of Iwahori-equivariant perverse sheaves on the thin and thick affine flag varieties associated to a split reductive group $G$. An earlier work of…

Under some technical assumptions, and building on joint work with Bezrukavnikov, we prove a multiplicity formula for indecomposable tilting perverse sheaves on affine flag varieties, with coefficients in a field of characteristic $p$, in…

We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${\mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element…

Under some assumptions we prove that the Deligne tensor product of categories of constructible perverse sheaves on pseudomanifolds X and Y is the category of constructible perverse sheaves on X\times Y. The Deligne external tensor product…

In this sequel of arXiv:1211.5294 and arXiv:1211.5948, we develop an adic formalism for \'etale cohomology of Artin stacks and prove several desired properties including the base change theorem. In addition, we define perverse t-structures…