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Transactions of the American Mathematical Society

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Stacks similar to the stack of perverse sheaves

Author: David Treumann
Journal: Trans. Amer. Math. Soc. 362 (2010), 5395-5409
MSC (2010): Primary 32S60
Published electronically: May 20, 2010
MathSciNet review: 2657685
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Abstract: We introduce, on a topological space $ X$, a class of stacks of abelian categories we call ``stacks of type P''. This class of stacks includes the stack of perverse sheaves (of any perversity, constructible with respect to a fixed stratification) and is singled out by fairly innocuous axioms. We show that some basic structure theory for perverse sheaves holds for a general stack of type P: such a stack is locally equivalent to a MacPherson-Vilonen construction, and under certain connectedness conditions its category of global objects is equivalent to the category of modules over a finite-dimensional algebra. To prove these results we develop a rudimentary tilting formalism for stacks of type P--another sense in which these stacks are ``similar to stacks of perverse sheaves''.

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Additional Information

David Treumann
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208

Received by editor(s): October 14, 2008
Published electronically: May 20, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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