Derived equivalences and equivariant Jordan decomposition

TL;DR

This paper extends the Bonnafé-Rouquier equivalence to include automorphisms of finite groups of Lie type and establishes a local version of this equivalence with similar properties.

Contribution

It introduces a lift of the Bonnafé-Rouquier equivalence to automorphisms and proves a local version with comparable features.

Findings

Extended equivalence to automorphisms of finite groups of Lie type

Proved existence of a local version of the equivalence

Maintained properties analogous to the original equivalence

Abstract

The Bonnaf\'e-Rouquier equivalence can be seen as a modular analogue of Lusztig's Jordan decomposition for groups of Lie type. In this paper, we show that this equivalence can be lifted to include automorphisms of the finite group of Lie type. Moreover, we prove the existence of a local version of this equivalence which satisfies similar properties.