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arXiv · 2308.16838

On cohomological characterizations of endotrivial modules

Fei Xu·Chenyou Zheng
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Abstract

Given a general finite group $G$, there are various finite categories whose cohomology theories are of great interests. Recently Balmer and Grodal gave some new characterizations of the groups of endotrivial modules, via \v{C}ech cohomology and category cohomology, respectively, defined on certain orbit categories. These two seemingly different approaches share a common root in topos theory. We shall demonstrate the connection, which leads to a better understanding as well as new characterizations of the group of endotrivial modules.

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Fei Xu, Chenyou Zheng. 2023-08-31. On cohomological characterizations of endotrivial modules. https://arxiv.org/abs/2308.16838

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