Integration of functions of motivic exponential class, uniform in all non-archimedean local fields of characteristic zero

DOI10.5802/jep.63zbMath1433.14012arXiv1510.08250OpenAlexW2963328820WikidataQ115479239 ScholiaQ115479239MaRDI QIDQ4559756

Immanuel Halupczok, Raf Cluckers

Publication date: 4 December 2018

Published in: Journal de l’École polytechnique — Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.08250

zbMATH Keywords

quantifier elimination\(p\)-adic integrationmotivic integrationnon-Archimedean geometrymotivic exponential functionsDenef-Pas cell decompositionmotivic Fourier transformsuniformity in all local fields

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Quantifier elimination, model completeness, and related topics (03C10) Arcs and motivic integration (14E18) Summability in abstract structures (40J99)

Related Items (7)

Motivic Wave Front Sets ⋮ Eliminating field quantifiers in strongly dependent henselian fields ⋮ WAVE FRONT HOLONOMICITY OF -CLASS DISTRIBUTIONS ON NON-ARCHIMEDEAN LOCAL FIELDS ⋮ Distributions and wave front sets in the uniform non‐archimedean setting ⋮ Evaluation of motivic functions, non-nullity, and integrability in fibers ⋮ On singularity properties of convolutions of algebraic morphisms ‐ the general case ⋮ Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

Cites Work

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• The wave front set of the Fourier transform of algebraic measures
• Fields with analytic structure
• The rationality of the Poincaré series associated to the p-adic points on a variety
• Relative elimination of quantifiers for Henselian valued fields
• Constructible motivic functions and motivic integration
• Constructible exponential functions, motivic Fourier transform and transfer principle
• Motivic integration on smooth rigid varieties and invariants of degenerations
• Integrability of oscillatory functions on local fields: transfer principles
• Motivic integration in all residue field characteristics for Henselian discretely valued fields of characteristic zero
• Motivic Serre invariants, ramification, and the analytic Milnor fiber
• The Serre invariant and the analytic Milnor fiber.
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Definable sets, motives and 𝑝-adic integrals
• Relative decidability and definability in henselian valued fields
• b-MINIMALITY
• p-adic semi-algebraic sets and cell decomposition.
• Cell Decomposition and Local Zeta Functions in a Tower of Unramified Extensions of a p -Adic Field
• On the Degree of Igusa's Local Zeta Function
• Uniform p-adic cell decomposition and local zeta functions.
• On definable subsets of p-adic fields
• Presburger sets and p-minimal fields
• Intégration motivique sur les schémas formels
• ORBITAL INTEGRALS FOR LINEAR GROUPS
• Decision procedures for real and p‐adic fields
• SOME PROPERTIES OF ANALYTIC DIFFERENCE VALUED FIELDS

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