On endosplit p-permutation resolutions and Broué's conjecture for p-solvable groups

2024/08/07 by Miller, Sam K. · 2 citations
#20C20 #20J05 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2408.04094

Abstract

Endosplit p-permutation resolutions play an instrumental role in verifying Broué's abelian defect group conjecture in numerous cases. In this article, we give a complete classification of endosplit p-permutation resolutions and reduce the question of Galois descent of an endosplit p-permutation resolution to the Galois descent of the module it resolves. This is shown using techniques from the study of endotrivial complexes, the invertible objects of the bounded homotopy category of p-permutation modules. As an application, we show that a refinement of Broué's conjecture proposed by Kessar and Linckelmann holds for blocks of p-solvable groups G satisfying G = O_p',p,p'(G).

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• On RoCK blocks of double covers of symmetric and alternating groups and the refined Broué conjecture
• The Euler characteristic of an endotrivial complex

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