Existential uniform $p$-adic integration and descent for integrability and largest poles

Cluckers, Raf; Stout, Mathias

Type de document :

Pré-publication ou Document de travail

Titre :

Existential uniform $p$-adic integration and descent for integrability and largest poles

Auteur(s) :

Cluckers, Raf [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Stout, Mathias [Auteur]

Date de publication :

2023-04-24

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Since the work by Denef, $p$-adic cell decomposition provides a well-established method to study $p$-adic and motivic integrals. In this paper, we present a variant of this method that keeps track of existential quantifiers. ...
Lire la suite >Since the work by Denef, $p$-adic cell decomposition provides a well-established method to study $p$-adic and motivic integrals. In this paper, we present a variant of this method that keeps track of existential quantifiers. This enables us to deduce descent properties for $p$-adic integrals. In particular, we show that integrability for `existential' functions descends from any $p$-adic field to any $p$-adic subfield. As an application, we obtain that the largest pole of the Serre-Poincar\'e series can only increase when passing to field extensions. As a side result, we prove a relative quantifier elimination statement for Henselian valued fields of characteristic zero that preserves existential formulas.Lire moins >

Langue :

Anglais

Commentaire :

38 pages

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

2304.12267
Accès libre
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