Perverse coherent sheaves on the nilpotent cone in good characteristic

TL;DR

This paper extends known results about perverse coherent sheaves on the nilpotent cone from characteristic zero to good positive characteristic, showing they are quasi-hereditary and derived-equivalent in this setting.

Contribution

It proves that graded versions of these properties hold for perverse coherent sheaves in good positive characteristic, generalizing prior characteristic zero results.

Findings

Perverse coherent sheaves are quasi-hereditary in good positive characteristic.

Derived equivalence with coherent sheaves extends to positive characteristic.

Results mirror characteristic zero case in the graded setting.

Abstract

In characteristic zero, Bezrukavnikov has shown that the category of perverse coherent sheaves on the nilpotent cone of a simply connected semisimple algebraic group is quasi-hereditary, and that it is derived-equivalent to the category of (ordinary) coherent sheaves. We prove that graded versions of these results also hold in good positive characteristic.