Perverse Sheaves and Ic-modules. the Koszul Case
نویسندگان
چکیده
For a stratified topological space we introduce the category of (mixed) IC-modules which are linear algebra devices with the relations described by the equation d = 0. We prove that the category of (mixed) IC-modules is equivalent to the category of (mixed) perverse sheaves for flag varieties.
منابع مشابه
Perverse Sheaves, Koszul Ic-modules, and the Quiver for the Category O
For a stratified topological space we introduce the category of IC-modules, which are linear algebra devices with the relations described by the equation d = 0. We prove that the category of (mixed) IC-modules is equivalent to the category of (mixed) perverse sheaves for flag varieties. As an application, we describe an algorithm calculating the quiver underlying the BGG category O for arbitrar...
متن کاملSheaves on Triangulated Spaces and Koszul Duality
Let X be a finite connected simplicial complex, and let δ be a perversity (i.e., some function from integers to integers). One can consider two categories: (1) the category of perverse sheaves cohomologically constructible with respect to the triangulation, and (2) the category of sheaves constant along the perverse simplices (δ-sheaves). We interpret the categories (1) and (2) as categories of...
متن کاملKoszul Duality and Mixed Hodge Modules
We prove that on a certain class of smooth complex varieties (those with “affine even stratifications”), the category of mixed Hodge modules is “almost” Koszul: it becomes Koszul after a few unwanted extensions are eliminated. We also give an equivalence between perverse sheaves on such a variety and modules for a certain graded ring, obtaining a formality result as a corollary. For flag variet...
متن کاملConstructible Sheaves on Simplicial Complexes and Koszul Duality
We obtain a linear algebra data presentation of the category Sh c (X,δ) of constructible with respect to perverse triangulation sheaves on a finite simplicial complex X. We also establish Koszul duality between Sh c (X, δ) and the category Mc(X, δ) of perverse sheaves constructible with respect to the triangulation
متن کاملPerverse Sheaves on a Triangulated Space
The goal of this note is to prove that the category of perverse sheaves constructible with respect to a triangulation is Koszul (i.e. equivalent to the category of finite-dimensional representations of a Koszul algebra). This result was conjectured by M. Vybornov in the framework of the general theory of cellular perverse sheaves due to R. MacPherson [4], [5]. Acknowledgments. I am grateful to ...
متن کامل