On the cohomology of pro-fusion systems

preprint2021arXivOpen access

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 $\text{GL}_2(\mathbb{Z}_p)$ for any odd prime $p$ .

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On the cohomology of pro-fusion systems

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