On the quasi-hereditary property for staggered sheaves

TL;DR

This paper explores the structure of staggered sheaves on algebraic varieties with group actions, establishing their categorical properties and constructing fundamental objects like standards and costandards.

Contribution

It introduces standard and costandard objects in the category of staggered sheaves and proves the existence of enough projectives and injectives.

Findings

Construction of standard and costandard objects

Proof of enough projectives and injectives in the category

Enhanced understanding of categorical properties of staggered sheaves

Abstract

Let G be an algebraic group over an algebraically closed field, acting on a variety X with finitely many orbits. "Staggered sheaves" are certain complexes of G-equivariant coherent sheaves on X that seem to possess many remarkable properties. In this paper, we construct "standard" and "costandard" objects in the category of staggered sheaves, and we prove that that category has enough projectives and injectives.