Around the Zilber-Pink Conjecture for Shimura Varieties

Autor: Ren, Jinbo

Publikováno v: Number Theory [math.NT]. Université Paris Saclay (COmUE), 2018. English. ⟨NNT : 2018SACLS208⟩

In this thesis, we study some arithmetic and geometric problems for Shimura varieties. This thesis consists of three parts. In the first part, we study some applications of model theory to number theory. In 2014, Pila and Tsimerman gave a proof of th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::c1fb9419605e16c2086981c303f7d461
https://tel.archives-ouvertes.fr/tel-01883648

Le théorème d’Ax-Lindemann mixte et ses applications à la conjecture de Zilber-Pink

Autor: Gao, Ziyang

Publikováno v: None
Mathématiques générales [math.GM]. Université Paris Sud-Paris XI; Universiteit Leiden (Leyde, Pays-Bas), 2014. Français. ⟨NNT : 2014PA112347⟩

The Zilber-Pink conjecture is a diophantine conjecture concerning unlikely intersections in mixed Shimura varieties. It is a common generalization of the André-Oort conjecture and the Mordell-Lang conjecture. This dissertation is aimed to study the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::00fd0481d6332308d53294c1605e960b
http://hdl.handle.net/1887/29841

Modèle complétude des structures o-minimales polynomialement bornées

Autor: Olivier Le Gal

Publikováno v: Mathématiques [math]. Université Rennes 1, 2006. Français
Mathématiques [math]. Université Rennes 1, 2006. Français. ⟨NNT : ⟩

O-minimal structures were introduced in the 80' by Van den Dries answering the Grotendick's request for a tame geomety framework, and were largely studied by Wilkie and Macintyre. This thesis shows an explicit theorem of the complement for o-minimal

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5cbef0783bc117c2aad70f2c0eb276dc
https://tel.archives-ouvertes.fr/tel-00127811/file/these.pdf

Quasi-analycité, o-minimalité et élimination des quantificateurs

Autor: Rambaud, Alexandre

Publikováno v: Logique [math.LO]. Univeristé Paris Diderot Paris 7, 2005. Français

This thesis studies from the point of view of model theory and topology certain classes of real functions : restricted quasi-analytic functions. Here, a restricted quasi-analytic class E will consist on the one hand of a ring of real functions C ∞,

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od______2592::3ec6cf45b9bfabbbcd526172283357f0
https://hal.archives-ouvertes.fr/tel-01257634