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- W4367000471 abstract "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." @default.
- W4367000471 created "2023-04-27" @default.
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- W4367000471 date "2023-04-24" @default.
- W4367000471 modified "2023-09-25" @default.
- W4367000471 title "Existential uniform $p$-adic integration and descent for integrability and largest poles" @default.
- W4367000471 doi "https://doi.org/10.48550/arxiv.2304.12267" @default.
- W4367000471 hasPublicationYear "2023" @default.
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