Can I read On endosplit $p$-permutation resolutions and Brou\'{e}'s conjecture for $p$-solvable groups on EtoBox?

On endosplit $p$-permutation resolutions and Brou\'{e}'s conjecture for $p$-solvable groups by Miller, Sam K. is a scholarly article available to read on EtoBox.

What is On endosplit $p$-permutation resolutions and Brou\'{e}'s conjecture for $p$-solvable groups about?

Endosplit $p$-permutation resolutions play an instrumental role in verifying Brou\'{e}'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 Brou\'{e}'s conjecture proposed by Kessar and Linckelmann holds for all blocks of $p$-solvable groups.

Author

Miller, Sam K.

Published

2024

Language

EN