Finite presentation of the tame fundamental group

Let p be a prime number, and let k be an algebraically closed field of characteristic p . We show that the tame fundamental group of a smooth affine curve over k is a projective profinite group. We prove that the fundamental group of a smooth projective variety over k is finitely presented; more gen...

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Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2022-05, Vol.28 (2), Article 37
Main Authors: Esnault, Hélène, Shusterman, Mark, Srinivas, Vasudevan
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Prime numbers
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Summary:Let p be a prime number, and let k be an algebraically closed field of characteristic p . We show that the tame fundamental group of a smooth affine curve over k is a projective profinite group. We prove that the fundamental group of a smooth projective variety over k is finitely presented; more generally, the tame fundamental group of a smooth quasi-projective variety over k , which admits a good compactification, is finitely presented.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-021-00732-4