Infinitesimal group schemes as iterative differential Galois groups
This article is concerned with Galois theory for iterative differential fields (ID-fields) in positive characteristic. More precisely, we consider purely inseparable Picard-Vessiot extensions, because these are the ones having an infinitesimal group scheme as iterative differential Galois group. In...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
17 March 2010
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| In: |
Journal of pure and applied algebra
Year: 2010, Jahrgang: 214, Heft: 11, Pages: 2092-2100 |
| ISSN: | 1873-1376 |
| DOI: | 10.1016/j.jpaa.2010.02.022 |
| Online-Zugang: | Resolving-System, Volltext: http://dx.doi.org/10.1016/j.jpaa.2010.02.022 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0022404910000551 
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| Verfasserangaben: | Andreas Maurischat |
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| 520 | |a This article is concerned with Galois theory for iterative differential fields (ID-fields) in positive characteristic. More precisely, we consider purely inseparable Picard-Vessiot extensions, because these are the ones having an infinitesimal group scheme as iterative differential Galois group. In this article we prove a necessary and sufficient condition to decide whether an infinitesimal group scheme occurs as Galois group scheme of a Picard-Vessiot extension over a given ID-field or not. In particular, this solves the inverse ID-Galois problem for infinitesimal group schemes. Furthermore, this gives a tool to tell whether all purely inseparable ID-extensions are in fact Picard-Vessiot extensions. | ||
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