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arXiv · 0908.3772

Infinitesimal group schemes as iterative differential Galois groups

Andreas Maurischat
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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.

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Andreas Maurischat. 2009-08-26. Infinitesimal group schemes as iterative differential Galois groups. https://doi.org/10.1016/j.jpaa.2010.02.022

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