Finite presentation of the tame fundamental group

Hélène Esnault; Mark Shusterman; Vasudevan Srinivas

Finite presentation of the tame fundamental group

Algebraic Geometry 2021-03-09 v2 Number Theory

Authors: Hélène Esnault , Mark Shusterman , Vasudevan Srinivas

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.

Keywords

tame fundamental group projective profinite group smooth affine curve smooth projective variety finite presentation good compactification quasi-projective variety

Cite

@article{arxiv.2102.13424,
  title  = {Finite presentation of the tame fundamental group},
  author = {Hélène Esnault and Mark Shusterman and Vasudevan Srinivas},
  journal= {arXiv preprint arXiv:2102.13424},
  year   = {2021}
}

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19 pages

Finite presentation of the tame fundamental group

Abstract

Keywords

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