Galois theory of differential schemes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912645169283072 |
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| author | Tomašić, Ivan Noohi, Behrang |
| author_facet | Tomašić, Ivan Noohi, Behrang |
| contents | Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of precategorical descent applied to algebraic-geometric situations, we develop a Galois theory that applies to morphisms of differential schemes, and vastly generalises the linear Picard-Vessiot theory, as well as the strongly normal theory of Kolchin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Galois theory of differential schemes Tomašić, Ivan Noohi, Behrang Algebraic Geometry Commutative Algebra Category Theory 12H05, 18F20, 18D40, 18E50, 14L30 Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of precategorical descent applied to algebraic-geometric situations, we develop a Galois theory that applies to morphisms of differential schemes, and vastly generalises the linear Picard-Vessiot theory, as well as the strongly normal theory of Kolchin. |
| title | Galois theory of differential schemes |
| topic | Algebraic Geometry Commutative Algebra Category Theory 12H05, 18F20, 18D40, 18E50, 14L30 |
| url | https://arxiv.org/abs/2407.21147 |