Galois descent of equivalences between blocks of $p$-nilpotent groups

TL;DR

This paper establishes conditions under which blocks of p-nilpotent groups are equivalent to their Brauer correspondents using Galois descent, advancing the understanding of modular representation theory.

Contribution

It provides new sufficient conditions for splendid Rickard and p-permutation equivalences between blocks and their Brauer correspondents, including Galois descent results for general groups.

Findings

Conditions for Rickard equivalence of p-blocks in p-nilpotent groups.

Galois descent results for p-permutation modules.

Applicability to arbitrary groups.

Abstract

We give sufficient conditions on $p$-blocks of $p$-nilpotent groups over $\mathbb{F}_p$ to be splendidly Rickard equivalent and $p$-permutation equivalent to their Brauer correspondents. The paper also contains Galois descent results on $p$-permutation modules and $p$-permutation equivalences that hold for arbitrary groups.