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
DOI: https://doi.org/10.1090/jag/707
Published electronically: June 29, 2018
MathSciNet review: 3846552
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Abstract | References | Additional Information

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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Additional Information

Mohamed Saïdi
Affiliation: College of Engineering, Mathematics and Physical Sciences, Harrison Building, University of Exeter, North Park Road, Exeter EX4 4QF, United Kingdom
Email: m.saidi@exeter.ac.uk

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.