Infinitesimal group schemes as iterative differential Galois groups

Details Infinitesimal group schemes as iterative differential Galois groups Infinitesimal group schemes as iterative differential Galois groups

2009-08-26

arxiv.org/abs/0908.3772v1

Journal of Pure and Applied Algebra 214 (2010), no. 11, pp. 2092-2100

Mathematics

Rings and Algebras

13 pages

Scientific paper

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.

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