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arXiv · 1603.04231

Multivariable (ϕ,Γ)-modules and products of Galois groups

Gergely Zábrádi
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Abstract

We show that the category of continuous representations of the $d$th direct power of the absolute Galois group of $\mathbb{Q}_p$ on finite dimensional $\mathbb{F}_p$-vector spaces (resp. finitely generated $\mathbb{Z}_p$-modules, resp. finite dimensional $\mathbb{Q}_p$-vector spaces) is equivalent to the category of étale $(φ,Γ)$-modules over a $d$-variable Laurent-series ring over $\mathbb{F}_p$ (resp. over $\mathbb{Z}_p$, resp. over $\mathbb{Q}_p$).

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BibTeXRIS

Gergely Zábrádi. 2016-12-20. Multivariable (ϕ,Γ)-modules and products of Galois groups. https://doi.org/10.4310/mrl.2018.v25.n2.a18

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