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arXiv · 1605.03876

Etale fundamental groups of affinoid $p$-adic curves

Mohamed Saidi
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Abstract

We prove that the geometric etale fundamental group of a (geometrically connected) rigid smooth $p$-adic affinoid curve is a semi-direct factor of a certain profinite free group. We also prove that the maximal pro-$p$ (resp. maximal prime-to-$p$) quotient of this geometric étale fundamental group is pro-$p$ free of infinite rank (resp. (pro-)prime-to-$p$ free of finite computable rank).

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Mohamed Saidi. 2017-08-26. Etale fundamental groups of affinoid $p$-adic curves. https://arxiv.org/abs/1605.03876

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