Projective varieties have countably many real forms
In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. We more generally prove it when the field of reals is replaced with a field that has only countably many finite extensions up to isomorphism. The verification consists in gathering known resul...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.441/ |
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| _version_ | 1825206206173544448 |
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| author | Labinet, Timothée L. |
| author_facet | Labinet, Timothée L. |
| author_sort | Labinet, Timothée L. |
| collection | DOAJ |
| description | In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. We more generally prove it when the field of reals is replaced with a field that has only countably many finite extensions up to isomorphism. The verification consists in gathering known results about automorphism groups and Galois cohomology. This contrasts with the recent discovery by A. Bot of an affine real variety with uncountably many real forms. |
| format | Article |
| id | doaj-art-0778b0aaaa484dbfbee0ef57ad2ef6ca |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-0778b0aaaa484dbfbee0ef57ad2ef6ca2025-02-07T11:08:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-07-01361G586386710.5802/crmath.44110.5802/crmath.441Projective varieties have countably many real formsLabinet, Timothée L.In this note, we check that a complex projective algebraic variety has (at most) countably many real forms. We more generally prove it when the field of reals is replaced with a field that has only countably many finite extensions up to isomorphism. The verification consists in gathering known results about automorphism groups and Galois cohomology. This contrasts with the recent discovery by A. Bot of an affine real variety with uncountably many real forms.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.441/ |
| spellingShingle | Labinet, Timothée L. Projective varieties have countably many real forms Comptes Rendus. Mathématique |
| title | Projective varieties have countably many real forms |
| title_full | Projective varieties have countably many real forms |
| title_fullStr | Projective varieties have countably many real forms |
| title_full_unstemmed | Projective varieties have countably many real forms |
| title_short | Projective varieties have countably many real forms |
| title_sort | projective varieties have countably many real forms |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.441/ |
| work_keys_str_mv | AT labinettimotheel projectivevarietieshavecountablymanyrealforms |