Purity and decomposition theorems for staggered sheaves
نویسندگان
چکیده
منابع مشابه
Introduction to Staggered Sheaves
This note is an expository account of the theory of staggered sheaves, based on a series of lectures given by the author at RIMS (Kyoto) in October 2008. Perverse sheaves have become a tool of great importance in representation theory, largely because of the remarkable way in which they provide a link between geometry and algebra. A single perverse sheaf contains information reminiscent of clas...
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The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial orbit in a simple Lie algebra. This work has applications to modular representation theory, for Weyl g...
متن کاملStaggered Sheaves on Partial Flag Varieties
Staggered t-structures are a class of t-structures on derived categories of equivariant coherent sheaves. In this note, we show that the derived category of coherent sheaves on a partial flag variety, equivariant for a Borel subgroup, admits an artinian staggered t-structure. As a consequence, we obtain a basis for its equivariant K-theory consisting of simple staggered sheaves. Let X be a vari...
متن کاملOn the Quasi-hereditary Property for Staggered Sheaves
Let G be an algebraic group over an algebraically closed field, acting on a variety X with finitely many orbits. Staggered sheaves are certain complexes of G-equivariant coherent sheaves on X that seem to possess many remarkable properties. In this paper, we construct “standard” and “costandard” objects in the category of staggered sheaves, and we prove that that category has enough projectives...
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Let X be a scheme, and let G be an affine group scheme acting on X. Under reasonable hypotheses on X and G, we construct a t-structure on the derived category of G-equivariant coherent sheaves that in many ways resembles the perverse coherent t-structure, but which incorporates additional information from the G-action. Under certain circumstances, the heart of this t-structure, called the “stag...
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ژورنال
عنوان ژورنال: Journal of the Institute of Mathematics of Jussieu
سال: 2012
ISSN: 1474-7480,1475-3030
DOI: 10.1017/s1474748011000211