Connections on trivial vector bundles over projective schemes
Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of this idea by restricting attention to connections on trivial...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.532/ |
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| author | Biswas, Indranil Hô Hai, Phùng dos Santos, Joao Pedro |
| author_facet | Biswas, Indranil Hô Hai, Phùng dos Santos, Joao Pedro |
| author_sort | Biswas, Indranil |
| collection | DOAJ |
| description | Over a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of this idea by restricting attention to connections on trivial vector bundles and replacing the fundamental group by a certain Lie algebra constructed from the regular forms. In more detail, we show that the differential Galois group is a certain “closure” of the aforementioned Lie algebra. |
| format | Article |
| id | doaj-art-93db5d854a25407181a631dc16237ce8 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-93db5d854a25407181a631dc16237ce82025-02-07T11:19:54ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G330932510.5802/crmath.53210.5802/crmath.532Connections on trivial vector bundles over projective schemesBiswas, Indranil0Hô Hai, Phùng1dos Santos, Joao Pedro2School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, IndiaInstitute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, VietnamInstitut de Mathématiques de Jussieu – Paris Rive Gauche, 4 place Jussieu, Case 247, 75252 Paris Cedex 5, FranceOver a smooth and proper complex scheme, the differential Galois group of an integrable connection may be obtained as the closure of the transcendental monodromy representation. In this paper, we employ a completely algebraic variation of this idea by restricting attention to connections on trivial vector bundles and replacing the fundamental group by a certain Lie algebra constructed from the regular forms. In more detail, we show that the differential Galois group is a certain “closure” of the aforementioned Lie algebra.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.532/ |
| spellingShingle | Biswas, Indranil Hô Hai, Phùng dos Santos, Joao Pedro Connections on trivial vector bundles over projective schemes Comptes Rendus. Mathématique |
| title | Connections on trivial vector bundles over projective schemes |
| title_full | Connections on trivial vector bundles over projective schemes |
| title_fullStr | Connections on trivial vector bundles over projective schemes |
| title_full_unstemmed | Connections on trivial vector bundles over projective schemes |
| title_short | Connections on trivial vector bundles over projective schemes |
| title_sort | connections on trivial vector bundles over projective schemes |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.532/ |
| work_keys_str_mv | AT biswasindranil connectionsontrivialvectorbundlesoverprojectiveschemes AT hohaiphung connectionsontrivialvectorbundlesoverprojectiveschemes AT dossantosjoaopedro connectionsontrivialvectorbundlesoverprojectiveschemes |