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Théorie des modèles des corps munis d'une dérivation de Hasse

Abstract : We study the fields with a Hasse derivation, via model-theory. In the first two parts, some algebraic facts about Hasse derivation are given, as well as model-theoretic facts about existentially closed Hasse fields (axioms, stability,...). We introduce in the third part an analogue of algebraic geometry suitable for the study of Hasse derivation; it is used to describe definable objects in our structures (using prolongations, D-structures...). We focus in the fourth part on the particular case of infinitely definable subgroups in algebraic groups. The fifth part deals with the characteristic zero case, specially with the various notions of rank.
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Contributor : Franck Benoist <>
Submitted on : Monday, March 5, 2007 - 4:30:55 PM
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  • HAL Id : tel-00134889, version 1



Franck Benoist. Théorie des modèles des corps munis d'une dérivation de Hasse. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2005. Français. ⟨tel-00134889⟩



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