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Iterative differential Galois theory in positive characteristic: A model theoretic approach

Published online by Cambridge University Press:  12 March 2014

Javier Moreno
Javier Moreno*
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon1, 43 Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France, E-mail: [email protected], URL: http://math.univ-lyonl.fr/~moreno/
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Abstract

This paper introduces a natural extension of Kolchin's differential Galois theory to positive characteristic iterative differential fields, generalizing to the non-linear 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 125 - 142
Copyright
Copyright © Association for Symbolic Logic 2011

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