Non-unipotent character sheaves as a categorical centre

TL;DR

This paper classifies character sheaves on a reductive group over an algebraic closure of a finite field using categorical centers, extending known classifications beyond unipotent cases and complex fields.

Contribution

It provides a categorical classification of non-unipotent character sheaves on reductive groups over finite fields, broadening previous results.

Findings

Classification of character sheaves as a categorical centre

Extension of known classifications to non-unipotent sheaves

Unified framework for finite field and complex cases

Abstract

Let G be a reductive connected group over the algebraic closure of a finite field. In this paper we give the classification of character sheaves on G in categorical terms (as a categorical centre). Previously such a classification was known for unipotent character sheaves and also in the case where the ground field is replaced by the complex numbers.