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

Cluckers, Raf; Stout, Mathias

Document type :

Pré-publication ou Document de travail

Title :

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

Author(s) :

Cluckers, Raf [Auteur]

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

Publication date :

2023-04-24

HAL domain(s) :

Mathématiques [math]

English abstract : [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. ...
Show more >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.Show less >

Language :

Anglais

Comment :

38 pages

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2304.12267
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