On the finite inverse problem in iterative differential Galois theory

Details On the finite inverse problem in iterative differential Galois theory On the finite inverse problem in iterative differential Galois theory

2010-07-21

arxiv.org/abs/1007.3648v2

Mathematics

Commutative Algebra

8 pages, v2: added "finite" in the title to be more precise. Changed some typos and also did some more explanations in some pr

Scientific paper

In positive characteristic, nearly all Picard-Vessiot extensions are inseparable over some intermediate iterative differential extensions. In the Galois correspondence, these intermediate fields correspond to nonreduced subgroup schemes of the Galois group scheme. Moreover, the Galois group scheme itself may be nonreduced, or even infinitesimal. In this article, we investigate which finite group schemes occur as iterative differential Galois group schemes over a given ID-field. For a large class of ID-fields, we give a description of all occuring finite group schemes.

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