2023/04/24 by Raf Cluckers, Cluckers, Raf, Mathias Stout +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Logic (math.LO) #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2304.12267
openalex publication_date 2023/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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-Poincaré 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.