On the Cohomology of Pro-Fusion Systems

Diaz Ramos, Antonio and Garaialde Ocana, Oihana and Mazza, Nadia and Park, Sejong (2023) On the Cohomology of Pro-Fusion Systems. Journal of Algebra and Its Applications, 22 (11): 2350243. ISSN 0219-4988

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Abstract

We prove the Cartan-Eilenberg stable elements theorem and construct a Lyndon-Hochschild-Serre type spectral sequence for pro-fusion systems. As an application, we determine the continuous mod-p cohomology ring of GL2(ℤp) for any odd prime p.