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Moreno, Javier

Iterative differential Galois theory in positive characteristic: a model theoretic approach. (English) Zbl 1225.03041

J. Symb. Log. 76, No. 1, 125-142 (2011).
Summary: This paper introduces a natural extension of Kolchin’s differential Galois theory to positive characteristic iterative differential fields, generalizing to the nonlinear case the iterative Picard-Vessiot theory recently developed by Matzat and van der Put. We use the methods and framework provided by the model theory of iterative differential fields. We offer a definition of strongly normal extension of iterative differential fields, and then prove that these extensions have good Galois theory and that a \(G\)-primitive element theorem holds. In addition, making use of the basic theory of arc spaces of algebraic groups, we define iterative logarithmic equations, finally proving that our strongly normal extensions are Galois extensions for these equations.

Cited in 1 Document

MSC:

03C60 Model-theoretic algebra
12H05 Differential algebra

Keywords:

differential Galois theory; iterative differential fields; iterative Picard-Vessiot theory; \(G\)-primitive element theorem; iterative logarithmic equations; Galois extensions
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\textit{J. Moreno}, J. Symb. Log. 76, No. 1, 125--142 (2011; Zbl 1225.03041)
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