The Intersection Cohomology and Derived Category of Algebraic Stacks

Abstract

The present paper provides an extension of the theory of perverse sheaves to algebraic stacks and therefore to moduli problems ℚ-varieties, algebraic spaces, etc. We also include a detailed study of the intersection cohomology of algebraic stacks and their associated moduli spaces. Smooth group scheme actions on singular varieties and the associated derived category turn up as special cases of the more general results on algebraic stacks.