Fundamental groups of proper varieties are finitely presented
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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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-02-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.518/ |
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| author | Lara, Marcin Srinivas, Vasudevan Stix, Jakob |
| author_facet | Lara, Marcin Srinivas, Vasudevan Stix, Jakob |
| author_sort | Lara, Marcin |
| collection | DOAJ |
| description | 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 $k$. |
| format | Article |
| id | doaj-art-940a231f8d2442f78ec378daf912f08e |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-940a231f8d2442f78ec378daf912f08e2025-02-07T11:12:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-02-01362G1515410.5802/crmath.51810.5802/crmath.518Fundamental groups of proper varieties are finitely presentedLara, Marcin0https://orcid.org/0000-0002-6766-6996Srinivas, Vasudevan1Stix, Jakob2Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, PolandTIFR, School of Mathematics, Homi Bhabha Road, Colaba, 400005 Mumbai, IndiaInstitut für Mathematik, Goethe–Universität Frankfurt, Robert-Mayer-Straße 6–8, 60325 Frankfurt am Main, GermanyIt 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 $k$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.518/ |
| spellingShingle | Lara, Marcin Srinivas, Vasudevan Stix, Jakob Fundamental groups of proper varieties are finitely presented Comptes Rendus. Mathématique |
| title | Fundamental groups of proper varieties are finitely presented |
| title_full | Fundamental groups of proper varieties are finitely presented |
| title_fullStr | Fundamental groups of proper varieties are finitely presented |
| title_full_unstemmed | Fundamental groups of proper varieties are finitely presented |
| title_short | Fundamental groups of proper varieties are finitely presented |
| title_sort | fundamental groups of proper varieties are finitely presented |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.518/ |
| work_keys_str_mv | AT laramarcin fundamentalgroupsofpropervarietiesarefinitelypresented AT srinivasvasudevan fundamentalgroupsofpropervarietiesarefinitelypresented AT stixjakob fundamentalgroupsofpropervarietiesarefinitelypresented |