Fundamental groups of proper varieties are finitely presented

Marcin Lara; Vasudevan Srinivas; Jakob Stix

doi:10.5802/crmath.518

Research article - Algebraic geometry

Fundamental groups of proper varieties are finitely presented

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

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 51-54.

Abstract
Résumé

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 $k$ .

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 $k$ .

Received: 2023-04-04
Revised: 2023-05-25
Accepted: 2023-05-25
Published online: 2024-02-02

DOI: 10.5802/crmath.518

Classification: 14F35, 14F20

Author's affiliations:

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

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Marcin Lara and Vasudevan Srinivas and Jakob Stix},
     title = {Fundamental groups of proper varieties are finitely presented},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {51--54},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {362},
     year = {2024},
     doi = {10.5802/crmath.518},
     language = {en},
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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/

References
Cited by

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