Perverse coherent sheaves (after Deligne)

TL;DR

This paper explores an analogue of perverse t-structures on derived categories of coherent sheaves, extending to equivariant sheaves and providing examples like sheaves on the nilpotent cone of a semi-simple group.

Contribution

It introduces a new perverse t-structure for coherent sheaves on schemes with dualizing complexes, including equivariant cases, and offers examples where coherent intersection cohomology sheaves are constructed.

Findings

Extension of perverse t-structure to equivariant coherent sheaves

Construction of coherent intersection cohomology sheaves in new contexts

Application to sheaves on the nilpotent cone of semi-simple groups

Abstract

This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends to the category of coherent sheaves equivariant under an action of an algebraic group; though proof of the general statement in this case does not require new ideas, it provides examples (such as sheaves on the nilpotent cone of a semi-simple group equivariant under the adjoint action) where construction of coherent "intersection cohomology" sheaves works.