| Type de publication : |
 |
Preprint, Working Paper, Document sans référence, etc. |
|
| Domaine : |
|
|
|
| Titre : |
|
Iterative differential Galois theory: a model theoretic approach |
|
| Auteur(s) : |
|
Javier Moreno ( ) 1 |
|
| Laboratoire : |
|
| 1 : |
Institut Camille Jordan (ICJ) |
|
|
CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées (INSA) - Lyon |
|
|
Bât. Jean Braconnier n° 101 43 Bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX |
|
|
France |
|
|
| Résumé : |
|
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. |
|
Langue du texte
intégral : |
|
Anglais |
|
Date de production,
écriture : |
|
04/2009 |
|
|
| Mots Clés : |
|
model theory – iterative derivations – differential Galois theory |
|
| Classification : |
|
MSC: Primary 03C98; Secondary 12H05 |
|
|
| Projet ANR : |
|
| Référence du projet |
ANR-06-CEXC-007 |
| Année |
2006 |
| Acronyme du projet |
THEMODMET |
| Titre du projet |
Théorie des modèles et indépendance dans les structures |
| Intitulé |
Programme "Chaires d'excellence |
| Acronyme de l'appel |
CEXC |
|
|
|
Récupérer au format
