On the quasi-hereditary property for staggered sheaves
نویسندگان
چکیده
منابع مشابه
On 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...
متن کاملIntroduction 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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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...
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We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site C. We use this to prove homotopy invariance and generalized descent statements for categories of sheaves and quasi-coherent sheaves. As a corollary we obtain an alternate proof of a generalized change of rings theorem of Hovey.
متن کاملSTAGGERED t-STRUCTURES ON DERIVED CATEGORIES OF EQUIVARIANT COHERENT SHEAVES
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: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-10-04996-2