 
Summary: PERVERSE COHERENT SHEAVES ON THE NILPOTENT CONE
IN GOOD CHARACTERISTIC
PRAMOD N. ACHAR
Abstract. In characteristic zero, Bezrukavnikov has shown that the cate
gory of perverse coherent sheaves on the nilpotent cone of a simply connected
semisimple algebraic group is quasihereditary, and that it is derivedequivalent
to the category of (ordinary) coherent sheaves. We prove that graded versions
of these results also hold in good positive characteristic.
1. Introduction
Let G be a simply connected semisimple algebraic group over an algebraically
closed field k of good characteristic. Let N denote the nilpotent variety in the Lie
algebra of G. There is a "scaling" action of Gm on N that commutes with the
Gaction. Following [B1], we may consider the category of (G × Gm)equivariant
perverse coherent sheaves on N, denoted PCohG×Gm
(N). This category has some
features in common with ordinary perverse sheaves, but it lives inside the derived
category of (equivariant) coherent sheaves. In this note, we prove the following two
homological facts about PCohG×Gm
(N).
Theorem 1.1. The category PCohG×Gm
