Parameterized D-torsors in differential Galois theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911483803205632 |
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| author | Sánchez, Omar León Meretzky, David |
| author_facet | Sánchez, Omar León Meretzky, David |
| contents | In the context of differential fields of characteristic zero with several commuting derivations, we discuss the notion of $\#$-differential equations on parameterized D-torsors and their associated Galois extensions. Using model-theoretic methods, we observe that any generalized strongly normal extension (in the sense of Pillay [14] and, more generally, León Sánchez [9]) is the Galois extension of a parameterized D-torsor. Furthermore, we prove a parameterized version of a theorem of Kolchin on differential cohomology, itself of independent interest, and use it to provide a necessary and sufficient cohomological condition for when a generalized strongly normal extension is the Galois extension for a log-differential equation on its Galois group (as a parameterized D-group). We also present general model-theoretic versions of some of the main results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_03658 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parameterized D-torsors in differential Galois theory Sánchez, Omar León Meretzky, David Logic In the context of differential fields of characteristic zero with several commuting derivations, we discuss the notion of $\#$-differential equations on parameterized D-torsors and their associated Galois extensions. Using model-theoretic methods, we observe that any generalized strongly normal extension (in the sense of Pillay [14] and, more generally, León Sánchez [9]) is the Galois extension of a parameterized D-torsor. Furthermore, we prove a parameterized version of a theorem of Kolchin on differential cohomology, itself of independent interest, and use it to provide a necessary and sufficient cohomological condition for when a generalized strongly normal extension is the Galois extension for a log-differential equation on its Galois group (as a parameterized D-group). We also present general model-theoretic versions of some of the main results. |
| title | Parameterized D-torsors in differential Galois theory |
| topic | Logic |
| url | https://arxiv.org/abs/2603.03658 |