Endotrivial representations of finite groups and equivariant line bundles on the Brown complex

We relate endotrivial representations of a finite group in characteristic $p$ to equivariant line bundles on the simplicial complex of nontrivial $p$ –subgroups, by means of weak homomorphisms.

Dedicated to Serge Bouc on the occasion of his 60th birthday

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Keywords

endotrivial modules, line bundles, Brown complex, Brown Quillen complex of $p$–subgroups, weak homomorphism

Mathematical Subject Classification 2010

Primary: 20C20, 55P91

References

Publication

Received: 23 May 2017

Accepted: 9 July 2018

Published: 6 December 2018

Proposed: Jesper Grodal

Seconded: Haynes R Miller, Mark Behrens

Authors

Paul Balmer
Mathematics Department UCLA Los Angeles, CA United States
http://www.math.ucla.edu/~balmer

Volume 22, issue 7 (2018)

Paul Balmer

Abstract