内平凡模的上同调刻画

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-05-02 DOI:10.1016/j.jalgebra.2025.04.021

Fei Xu, Chenyou Zheng

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引用次数: 0

摘要

给定一般有限群G，存在各种有限范畴，它们的上同调理论是人们非常感兴趣的。最近Balmer和Grodal分别通过Čech上同调和范畴上同调给出了在一定轨道范畴上定义的内平凡模群的一些新的表征。这两种看似不同的方法在拓扑理论中有着共同的根源。我们将证明这种联系，这将导致更好的理解以及对内模群的新特征。

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On cohomological characterizations of endotrivial modules

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 Čech 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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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.