Perverse coherent sheaves

TL;DR

This paper extends the concept of perverse sheaves to the derived category of coherent sheaves on algebraic stacks, enabling the construction of coherent intersection cohomology complexes under certain conditions.

Contribution

It introduces a new analogue of perverse sheaves in the setting of coherent sheaves on algebraic stacks, broadening the scope of intersection cohomology theory.

Findings

Construction of coherent intersection cohomology complexes under strong assumptions

Extension of perverse sheaves concept to algebraic stacks

Supersedes previous preprint arXiv:math/0005152

Abstract

We describe an analogue of the notion of a perverse sheaf in the setting of the derived category of coherent sheaves on an algebraic stack. Under strong additional assumptions the construction of coherent "intersection cohomology" complexes works. This paper supersedes the preprint arXiv:math/0005152 by the second author.