Comptes Rendus
Article de recherche - Géométrie algébrique
Fundamental groups of proper varieties are finitely presented
[Le groupe fondamental d’une variété propre est de présentation finie]
Marcin Lara1   ; Vasudevan Srinivas2 ; Jakob Stix3
1 Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
2 TIFR, School of Mathematics, Homi Bhabha Road, Colaba, 400005 Mumbai, India
3 Institut für Mathematik, Goethe–Universität Frankfurt, Robert-Mayer-Straße 6–8, 60325 Frankfurt am Main, Germany
Comptes Rendus. Mathématique, Volume 362 (2024), pp. 51-54.

Il a été prouvé dans [1], que le groupe fondamental étale d’une variété projective lisse connexe sur un corps algébriquement clos k est topologiquement de présentation finie. Dans cette note, nous étendons ce résultat à tous les schémas propres connexes sur k.

It was proven in [1], that the étale fundamental group of a connected smooth projective variety over an algebraically closed field k is topologically finitely presented. In this note, we extend this result to all connected proper schemes over k.

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DOI : 10.5802/crmath.518
Classification : 14F35, 14F20
Marcin Lara 1 ; Vasudevan Srinivas 2 ; Jakob Stix 3

1 Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
2 TIFR, School of Mathematics, Homi Bhabha Road, Colaba, 400005 Mumbai, India
3 Institut für Mathematik, Goethe–Universität Frankfurt, Robert-Mayer-Straße 6–8, 60325 Frankfurt am Main, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Fundamental groups of proper varieties are finitely presented},
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Marcin Lara; Vasudevan Srinivas; Jakob Stix. Fundamental groups of proper varieties are finitely presented. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 51-54. doi : 10.5802/crmath.518. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.518/

[1] Hélène Esnault; Mark Shusterman; Vasudevan Srinivas Finite presentation of the tame fundamental group, Sel. Math., New Ser., Volume 28 (2022) no. 2, 37, 19 pages | DOI | MR | Zbl

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