• Corpus ID: 119136023

Perverse Schobers

@inproceedings{Kapranov2014PerverseS,
  title={Perverse Schobers},
  author={Mikhail M. Kapranov and Vadim Schechtman},
  year={2014}
}
The notion of a perverse sheaf, introduced in [BBD], has come to play a central role in algebraic geometry and representation theory. In particular, appropriate categories of perverse sheaves provide “categorifications” of various representation spaces, these spaces being recovered as the Grothedieck groups of the categories. The goal of this paper is to suggest the possibility of categorifying the very concept of a perverse sheaf. In other words, we propose to develop a theory of perverse… 

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References

SHOWING 1-10 OF 32 REFERENCES

How to glue perverse sheaves

The aim of this note [0] is to give a short, self-contained account of the vanishing cycle constructions of perverse sheaves; e.g., for the needs of [1]. It differs somewhat from the alternative

Fukaya Categories as Categorical Morse Homology

The Fukaya category of a Weinstein manifold is an intricate symplectic inva- riant of high interest in mirror symmetry and geometric representation theory. This paper informally sketches how, in

Affine braid group actions on derived categories of Springer resolutions

In this paper we construct and study an action of the affine braid group associated to a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the

Tilting exercises

This is a geometry-oriented review of the basic formalism of tilting objects (originally due to Ringel, see [Ri], §5). In the first section we explain that tilting extensions form a natural framework

Braid groups and Kleinian singularities

We establish faithfulness of braid group actions generated by twists along an ADE configuration of 2-spherical objects in a derived category. Our major tool is the Garside structure on braid groups

Triangulated surfaces in triangulated categories

For a triangulated category A with a 2-periodic dg-enhancement and a triangulated oriented marked surface S we introduce a dg-category F(S,A) parametrizing systems of exact triangles in A labelled by

The Theory of Hyperfunctions on Totally Real Subsets of a Complex Manifold with Applications to Extension Problems

Introduction. Suppose K is a compact subset of a Stein manifold. The set K is said to be holomorphically convex if K is homeomorphic to the spectrum of the topological algebra of analytic functions

A vanishing theorem for Holonomic modules with positive characteristic varieties

Let M be a real analytic manifold, X a complexification of M, Ji a holonomic module over the ring $x of microdifferential operators and Char(Jt} its characteristic variety. We prove that if (T%fX,

Constructible sheaves and the Fukaya category

Let $X$ be a compact real analytic manifold, and let $T^*X$ be its cotangent bundle. Let $Sh(X)$ be the triangulated dg category of bounded, constructible complexes of sheaves on $X$. In this paper,