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2020 On étale fundamental groups of formal fibres of $p$-adic curves
Mohamed Saïdi
Tohoku Math. J. (2) 72(1): 63-76 (2020). DOI: 10.2748/tmj/1585101621

Abstract

We investigate a certain class of (geometric) finite (Galois) coverings of formal fibres of $p$-adic curves and the corresponding quotient of the (geometric) étale fundamental group. A key result in our investigation is that these (Galois) coverings can be compactified to finite (Galois) coverings of proper $p$-adic curves. We also prove that the maximal prime-to-$p$ quotient of the geometric étale fundamental group of a (geometrically connected) formal fibre of a $p$-adic curve is (pro-)prime-to-$p$ free of finite computable rank.

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Mohamed Saïdi. "On étale fundamental groups of formal fibres of $p$-adic curves." Tohoku Math. J. (2) 72 (1) 63 - 76, 2020. https://doi.org/10.2748/tmj/1585101621

Information

Published: 2020
First available in Project Euclid: 25 March 2020

zbMATH: 07199987
MathSciNet: MR4079424
Digital Object Identifier: 10.2748/tmj/1585101621

Subjects:
Primary: 14H30
Secondary: 11G20

Keywords: $p$-adic curves , étale fundamental groups , formal fibre

Rights: Copyright © 2020 Tohoku University

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Vol.72 • No. 1 • 2020
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