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arXiv · 2005.11887

Multivariable $(\varphi ,\Gamma )$-modules and Representations of Products of Galois Groups: The Case of Imperfect Residue Field

Jishnu Ray·Feng Wei·Gergely Zábrádi
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Abstract

Let $K$ be a complete discretely valued field with mixed characteristic $(0, p)$ and imperfect residue field $k_K$. Let $\Delta$ be a finite set. We construct an equivalence of categories between finite dimensional $\Bbb{F}_p$-representations of the product of $\Delta$ copies of the absolute Galois group of $K$ and multivariable \' etale $(\varphi, \Gamma)$-modules over a multivariable Laurent series ring over $k_K$.

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Jishnu Ray, Feng Wei, Gergely Zábrádi. 2020-05-25. Multivariable $(\varphi ,\Gamma )$-modules and Representations of Products of Galois Groups: The Case of Imperfect Residue Field. https://doi.org/10.24033/bsmf.2837

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