Infinitesimal group schemes as iterative differential Galois groups

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.

arXiv comment13 pages

References in corpus (1)

• The inverse problem of differential Galois theory over the field R(z)

Cited by in corpus (4)

• Picard-Vessiot theory of differentially simple rings
• Reduced group schemes as iterative differential Galois groups
• Non-free iterative differential modules
• Torsion group schemes as iterative differential Galois groups