Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Étale fundamental groups of affinoid $ p$-adic curves

Author: Mohamed Saïdi
Journal: J. Algebraic Geom. 27 (2018), 727-749
Published electronically: June 29, 2018
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Abstract: We prove that the geometric étale fundamental group of a (geometrically connected) rigid smooth $ p$-adic affinoid curve is a semi-direct factor of a certain profinite free group. We prove that the maximal pro-$ 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 Saïdi
Affiliation: College of Engineering, Mathematics and Physical Sciences, Harrison Building, University of Exeter, North Park Road, Exeter EX4 4QF, United Kingdom

Received by editor(s): August 11, 2016
Received by editor(s) in revised form: February 5, 2017, May 25, 2017, and June 7, 2017
Published electronically: June 29, 2018
Dedicated: In memory of Si M’hamed, my father
Article copyright: © Copyright 2018 University Press, Inc.

American Mathematical Society