The differential Galois group of the maximal prounipotent extension is free
Let F be a characteristic zero differential field with algebraically closed constant field, and consider the compositum F_u of all Picard–Vessiot extensions of F with unipotent differential Galois group. We prove that the group of F differential automorphisms of F_u is a free prounipotent group.
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2022-04, Vol.150 (4), p.1421-1433 |
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| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let F be a characteristic zero differential field with algebraically closed constant field, and consider the compositum F_u of all Picard–Vessiot extensions of F with unipotent differential Galois group. We prove that the group of F differential automorphisms of F_u is a free prounipotent group. |
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| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.1090/proc/15740 |