Hensel minimality II: Mixed characteristic and a diophantine application

Cluckers, Raf; Halupczok, Immanuel; Rideau-Kikuchi, Silvain; Vermeulen, Floris

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1017/fms.2023.91

Title :

Hensel minimality II: Mixed characteristic and a diophantine application

Author(s) :

Cluckers, Raf [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Halupczok, Immanuel [Auteur]
Heinrich Heine Universität Düsseldorf = Heinrich Heine University [Düsseldorf]
Rideau-Kikuchi, Silvain [Auteur]
Département de Mathématiques et Applications - ENS-PSL [DMA]
Centre National de la Recherche Scientifique [CNRS]
Vermeulen, Floris [Auteur]
Département de mathématique [Louvain]

Journal title :

Forum of Mathematics, Sigma

Publisher :

Cambridge University press

Publication date :

2023

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

We extend the results about Hensel minimality to include also the mixed characteristic case. This completes our axiomatic framework for tame non-archimedean geometry over Henselian valued fields of characteristic zero. We ...
Show more >We extend the results about Hensel minimality to include also the mixed characteristic case. This completes our axiomatic framework for tame non-archimedean geometry over Henselian valued fields of characteristic zero. We prove a Jacobian property, a strong form of Taylor approximations of definable functions, resplendency results and cell decomposition, all under 1-h-minimality. We obtain a diophantine application of counting rational points of bounded height on Hensel minimal curves.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Configurations géométriques et combinatoires en théorie des modèles

Collections :