Stacks similar to the stack of perverse sheaves
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."
Cite
@article{arxiv.0801.3016,
title = {Stacks similar to the stack of perverse sheaves},
author = {David Treumann},
journal= {arXiv preprint arXiv:0801.3016},
year = {2008}
}