Modular perverse sheaves on flag varieties II: Koszul duality and formality
نویسندگان
چکیده
Building on the theory of parity sheaves due to Juteau–Mautner– Williamson, we develop a formalism of “mixed modular perverse sheaves” for varieties equipped with a stratification by affine spaces. We then give two applications: (1) a “Koszul-type” derived equivalence relating a given flag variety to the Langlands dual flag variety, and (2) a formality theorem for the modular derived category of a flag variety (extending the main result of [RSW]).
منابع مشابه
Koszul 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 کاملKoszul Duality for Toric Varieties
We show that certain categories of perverse sheaves on affine toric varieties Xσ and Xσ∨ defined by dual cones are Koszul dual in the sense of Beilinson, Ginzburg and Soergel [BGS]. The functor expressing this duality is constructed explicitly by using a combinatorial model for mixed sheaves on toric varieties.
متن کاملModular perverse sheaves on flag varieties I: tilting and parity sheaves
In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group G is a “graded version” of the category of tilting perverse sheaves on the flag variety of the dual group Ǧ, for any field of coefficients whose characteristic is good for G. We derive some consequences on Soergel’s modular category O, and on multiplicities and decomposition n...
متن کاملPerverse Sheaves and Ic-modules. the Koszul Case
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.
متن کاملModular perverse sheaves on flag varieties III: positivity conditions
We further develop the general theory of the “mixed modular derived category” introduced by the authors in a previous paper in this series. We then use it to study positivity and Q-Koszulity phenomena on flag varieties.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014