Séminaires : Géométrie et Théorie des Modèles

Equipe(s) : lm,
Responsables :Zoé Chatzidakis, Raf Cluckers.
Email des responsables :
Salle :
Adresse :ENS
Description

http://www.logique.jussieu.fr/ zoe/GTM/

 

Pour recevoir le programme par e-mail, écrivez à : zchatzid_at_dma.ens.fr.Retour ligne automatique
Pour les personnes ne connaissant pas du tout de théorie des modèles, des notes introduisant les notions de base (formules, ensembles définissables, théorème de compacité, etc.) sont disponibles ici : http://www.logique.jussieu.fr/~zoe/papiers/MTluminy.dvi. Ces personnes peuvent aussi consulter les premiers chapitres du livre Model Theory and Algebraic Geometry, E. Bouscaren ed., Springer Verlag, Lecture Notes in Mathematics 1696, Berlin 1998.Retour ligne automatique
Les notes de quelques-uns des exposés sont disponibles.


Orateur(s) Eva Leenknegt - Leuven,
Titre Cell Decomposition for P-minimal structures: a story
Date10/02/2017
Horaire16:00 à 17:30
RésumeP-minimality is a concept that was developed by Haskell and Macpherson as a p-adic equivalent for o-minimality. For o-minimality, the cell decomposition theorem is probably one of the most powerful tools, so it is quite a natural question to ask for a p-adic equivalent of this.
In this talk I would like to give an overview of the development of cell decomposition in the p-adic context, with an emphasis on how questions regarding the existence of definable skolem functions have complicated things. The idea of p-adic cell decomposition was first developed by Denef, for p-adic semi-algebraic structures, as a tool to answer certain questions regarding quantifier elimination, rationality and p-adic integration. This first version eventually resulted in a cell decomposition theorem for P-minimal structures. This theorem, proven by Mourgues, was however dependent on the existence of definable Skolem functions. The second part of the talk will focus a bit more on Skolem functions, and sketch a generalized version of the Denef-Mourgues theorem that does not rely on the existence of such functions, by introducing a notion of clustered cells. We will explain the notion, give an informal sketch of the proof, and compare with other versions of cell decomposition.
Salle
AdresseENS
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