On the cohomology of pro-fusion systems

Antonio Díaz Ramos; Oihana Garaialde Ocaña; Nadia Mazza; Sejong Park

On the cohomology of pro-fusion systems

Algebraic Topology 2021-02-02 v2 Group Theory

Authors: Antonio Díaz Ramos , Oihana Garaialde Ocaña , Nadia Mazza , Sejong Park

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

Keywords

pro-fusion systems stable elements theorem spectral sequence continuous cohomology mod-p cohomology

Cite

@article{arxiv.2003.01626,
  title  = {On the cohomology of pro-fusion systems},
  author = {Antonio Díaz Ramos and Oihana Garaialde Ocaña and Nadia Mazza and Sejong Park},
  journal= {arXiv preprint arXiv:2003.01626},
  year   = {2021}
}

Comments

19 pages, 4 figures

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