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arXiv · 2102.13424

Finite presentation of the tame fundamental group

Hélène Esnault·Mark Shusterman·Vasudevan Srinivas
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Abstract

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 we prove that the tame fundamental group of a smooth quasi-projective variety over $k$ which admits a good compactification is finitely presented. v2: references added. Thank you to all for the friendly and fruitful comments.

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Hélène Esnault, Mark Shusterman, Vasudevan Srinivas. 2021-03-07. Finite presentation of the tame fundamental group. https://arxiv.org/abs/2102.13424

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