HAL : hal-00407562, version 1

arXiv : 0907.4559

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Iterative differential Galois theory: a model theoretic approach

Javier Moreno 1

(04/2009)

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.

1 :	Institut Camille Jordan (ICJ)
	CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon

Domaine

:

Mathématiques/Logique Mathématiques/Géométrie algébrique

Mots Clés : model theory – iterative derivations – differential Galois theory

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Contributeur : Javier Moreno <>

Soumis le : Dimanche 26 Juillet 2009, 14:32:44

Dernière modification le : Lundi 27 Juillet 2009, 10:28:16