Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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''.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 32S60

Retrieve articles in all journals with MSC (2010): 32S60


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-04958-X
PII: S 0002-9947(2010)04958-X
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.