Infinitesimal group schemes as iterative differential Galois groups

• Verfasst von: Maurischat, Andreas [VerfasserIn]
• Titel: Infinitesimal group schemes as iterative differential Galois groups
• Verf.angabe: Andreas Maurischat
• Umfang: 9 S.
• Fussnoten: Gesehen am 22.02.2019
• Titel Quelle: Enthalten in: Journal of pure and applied algebra
• Jahr Quelle: 2010
• Band/Heft Quelle: 214(2010), 11, S. 2092-2100
• ISSN Quelle: 1873-1376
• DOI: doi:10.1016/j.jpaa.2010.02.022
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1587937050

Abstract

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.