Character sheaves in characteristic $p$ have nilpotent singular support

TL;DR

This paper proves that character sheaves in positive characteristic have nilpotent singular support, extending prior work from characteristic zero to positive characteristic by introducing a new category of tame perverse sheaves.

Contribution

It introduces a category of tame perverse sheaves and demonstrates their properties to establish nilpotent singular support in positive characteristic.

Findings

Character sheaves have nilpotent singular support in any characteristic.

Introduction of a category of tame perverse sheaves.

Extension of known results to positive characteristic.

Abstract

We prove that character sheaves have nilpotent singular support in any characteristic, partially extending the work of Mirkovic, Vilonen and independently Ginzburg to positive characteristic. We do this by introducing a category of tame perverse sheaves and studying its properties.