Etale fundamental groups of affinoid $p$-adic curves
Algebraic Geometry
2017-08-29 v5 Number Theory
Abstract
We prove that the geometric etale fundamental group of a (geometrically connected) rigid smooth -adic affinoid curve is a semi-direct factor of a certain profinite free group. We also prove that the maximal pro- (resp. maximal prime-to-) quotient of this geometric \'etale fundamental group is pro- free of infinite rank (resp. (pro-)prime-to- free of finite computable rank).
Keywords
Cite
@article{arxiv.1605.03876,
title = {Etale fundamental groups of affinoid $p$-adic curves},
author = {Mohamed Saidi},
journal= {arXiv preprint arXiv:1605.03876},
year = {2017}
}
Comments
Final version, to appear in Journal of Algebraic Geometry