Parity sheaves and tilting modules
نویسندگان
چکیده
منابع مشابه
Modular 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 کاملMorse Theory and Tilting Sheaves
Tilting perverse sheaves arise in geometric representation theory as natural bases for many categories. (See [1] or Section 3 below for definitions and some background results.) For example, for category O of a complex reductive group G, tilting modules correspond to tilting sheaves on the Schubert stratification S of the flag variety B. In this setting, there are many characterizations of tilt...
متن کاملParity Sheaves
Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of “parity sheaves”, which are objects in the constructible derived category of sheaves with coefficients in an arbitrary field or complete discrete valuation ring. If X admits a resolution also satisfying a parity condition, then the direct image of the constant she...
متن کاملRigidity of Tilting Modules
Let Uq denote the quantum group associated with a finite dimensional semisimple Lie algebra. Assume that q is a complex root of unity of odd order and that Uq is obtained via Lusztig’s q-divided powers construction. We prove that all regular projective (tilting) modules for Uq are rigid, i.e., have identical radical and socle filtrations. Moreover, we obtain the same for a large class of Weyl m...
متن کاملTilting Modules and Universal Localization
We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R → RU at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form RU ⊕ RU/R. Furthermore, we discuss the relationship between universal localization and the localization R → QG given by a perfect Gabri...
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ژورنال
عنوان ژورنال: Annales scientifiques de l'École normale supérieure
سال: 2016
ISSN: 0012-9593,1873-2151
DOI: 10.24033/asens.2282