## 47 Citations

Perverse sheaves with nilpotent singular support on the stack of coherent sheaves on an elliptic curve

- Mathematics
- 2021

We define a stratification of the moduli stack of coherent sheaves on an elliptic curve which allows us (1) to give an explicit description of the irreducible components of the global nilpotent cone…

BEILINSON-BERNSTEIN LOCALIZATION

- Mathematics
- 2018

The purpose of this paper is to give an overview of the BeilinsonBernstein localization theorem. It is a major result which introduced new geometric methods into representation theory. The theorem…

An introduction to sheaf quantization

- Philosophy
- 2022

. The notion of sheaf quantization has many faces: an enhancement of the notion of constructible sheaves, the Betti counterpart of Fukaya–Floer theory, a topological realization of WKB-states in…

Equivalent definitions of Arthur packets for real quasisplit unitary groups

- Mathematics
- 2022

Mok has deﬁned Arthur packets for quasisplit unitary groups. His deﬁnition follows Arthur’s work on classical groups and relies on harmonic analysis. For real groups there is an alternative deﬁnition…

A generalization of the b-function lemma

- MathematicsCompositio Mathematica
- 2021

We establish some cohomological bounds in $D$-module theory that are known in the holonomic case and folklore in general. The method rests on a generalization of the $b$-function lemma for…

Absolute sets of rigid local systems

- Mathematics
- 2021

The absolute sets of local systems on a smooth complex algebraic variety are the subject of a conjecture of [BW] based on an analogy with special subvarieties of Shimura varieties. An absolute set…

Borel-Moore homology of determinantal varieties

- Mathematics
- 2021

Abstract. We compute the rational Borel–Moore homology groups for affine determinantal varieties in the spaces of general, symmetric, and skew-symmetric matrices, solving a problem suggested by the…

Estimates for zero loci of Bernstein-Sato ideals

- Mathematics
- 2021

We give estimates for the zero loci of Bernstein-Sato ideals. An upper bound is proved as a multivariate generalisation of the upper bound by Lichtin for the roots of Bernstein-Sato polynomials. The…

Generic Vanishing, 1-forms, and Topology of Albanese Maps

- Mathematics
- 2021

The goal of this article is to study global holomorphic 1-forms on smooth projective varieties. First, we establish an interesting link between the generic vanishing theory and the topology of the…

Generic vanishing and holomorphic 1-forms

- Mathematics
- 2021

The goal of this article is three-fold; first we establish an interesting link between some sets related to cohomologies of complex local systems and the stratification of the Albanese morphism of…

## References

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The decomposition theorem, perverse sheaves and the topology of algebraic maps

- Mathematics
- 2009

We give a motivated introduction to the theory of perverse sheaves, culminating in the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the…

D-Modules, Perverse Sheaves, and Representation Theory

- Mathematics
- 2007

D-Modules and Perverse Sheaves.- Preliminary Notions.- Coherent D-Modules.- Holonomic D-Modules.- Analytic D-Modules and the de Rham Functor.- Theory of Meromorphic Connections.- Regular Holonomic…

The Development of Intersection Homology Theory

- Mathematics
- 2007

58 pages, hypertext links added; appeared in Part 3 of the special issue of Pure and Applied Mathematics Quarterly in honor of Robert MacPherson. However, the flags in the margin were unfortunately…

Sheaves in Topology

- Mathematics
- 2004

1 Derived Categories.- 1.1 Categories of Complexes C*(A).- 1.2 Homotopical Categories K*(A).- 1.3 The Derived Categories D*(A).- 1.4 The Derived Functors of Hom.- 2 Derived Categories in Topology.-…

Morse theory for constructible sheaves

- Mathematics
- 2003

In this chapter we prove the basic results about stratified Morse theory in the framework of constructible sheaves. We follow the notions of Goresky-MacPherson so that one can easily compare our…

Singularities and Topology of Hypersurfaces

- Mathematics
- 1992

This book systematically presents a large number of basic results on the topology of complex algebraic varieties using the information on the local topology and geometry of a singularity. These…

The Riemann-Hilbert Problem for Holonomic Systems

- Mathematics
- 1984

On demontre l'equivalence de la categorie derivee des systemes holonomes et celle des faisceaux constructibles

Intersection homology II

- Mathematics
- 1983

In [19, 20] we introduced topological invariants IH~,(X) called intersection homology groups for the study of singular spaces X. These groups depend on the choice of a perversity p: a perversity is a…