Descent of splendid Rickard equivalences in alternating groups

TL;DR

This paper proves that blocks of alternating groups are splendidly Rickard equivalent to their Brauer correspondents, supporting a refined version of Broué's conjecture and advancing understanding of modular representation theory.

Contribution

It establishes splendid Rickard equivalences for blocks of alternating groups over complete discrete valuation rings, providing evidence for a refined Broué conjecture.

Findings

Blocks of alternating groups are splendidly Rickard equivalent to their Brauer correspondents.

Supports a refined version of Broué's abelian defect group conjecture.

Advances modular representation theory of symmetric and alternating groups.

Abstract

We show that each block of an alternating group over an arbitrary complete discrete valuation ring is splendidly Rickard equivalent to its Brauer correspondent. This provides new evidence for a refined version of Brou\'{e}'s abelian defect group conjecture proposed by Kessar and Linckelmann.