Galois cohomology of $p$-adic fields and $(\varphi, \tau)$-modules

Luming Zhao

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arXiv · 2201.11235

Galois cohomology of $p$-adic fields and $(\varphi, \tau)$-modules

Luming Zhao

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Abstract

We construct various explicit Herr complexes that compute the Galois cohomology of a $p$-adic representation of the absolute Galois group of a complete discrete valuation field of characteristic $0$ with a perfect residue field of characteristic $p$, using the associated $(\varphi,\tau)$-modules (defined by Xavier Caruso), instead of $(\varphi,\Gamma)$-modules. We also give an application to $p$-divisible groups.

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BibTeX RIS

Luming Zhao. 2022-01-26. Galois cohomology of $p$-adic fields and $(\varphi, \tau)$-modules. https://arxiv.org/abs/2201.11235

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