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Exact functors on perverse coherent sheaves

Part of: Abelian categories Local theory (Co)homology theory

Published online by Cambridge University Press:  04 May 2015

Clemens Koppensteiner
Clemens Koppensteiner*
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Rd, Evanston, IL 60208, USA email clemens@math.northwestern.edu
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Abstract

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Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if $R{\rm\Gamma}_{Z}{\mathcal{F}}$ is concentrated in degree $0$ for special subvarieties $Z$ of $X$. These subvarieties $Z$ are analogs of Lagrangians in the symplectic case.

Keywords

perverse coherent sheaveslocal cohomology

MSC classification

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions
Secondary: 18E30: Derived categories, triangulated categories 14B15: Local cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 9 , September 2015 , pp. 1688 - 1696
Copyright
© The Author 2015 

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