Stacks similar to the stack of perverse sheaves

2008/01/19 by David Treumann, Treumann, David · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0801.3016

openalex publication_date 2008/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Faisceaux pervers sur les variétés toriques lisses

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