Hensel minimality I
| Autor: | Raf Cluckers, Immanuel Halupczok, Silvain Rideau-Kikuchi |
|---|---|
| Přispěvatelé: | Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), University of Lille, Catholic University of Leuven - Katholieke Universiteit Leuven (KU Leuven), Heinrich Heine Universität Düsseldorf = Heinrich Heine University [Düsseldorf], Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), ANR-19-CE40-0022,GeoMod,Configurations géométriques et combinatoires en théorie des modèles(2019) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Taylor approximation Mathematics Applied T-CONVEXITY Mathematics - Algebraic Geometry HEIGHT cell decomposition FOS: Mathematics Discrete Mathematics and Combinatorics Number Theory (math.NT) Algebraic Geometry (math.AG) Mathematical Physics VOLUME GROWTH REAL Algebra and Number Theory Science & Technology Mathematics - Number Theory analogues to o-minimality tame geometry on Henselian valued fields O-MINIMALITY Mathematics - Logic Lipschitz continuity Non-Archimedean geometry DEFINABLE SETS [MATH.MATH-LO]Mathematics [math]/Logic [math.LO] quantifier elimination Physical Sciences LIPSCHITZ STRATIFICATIONS Geometry and Topology POINTS Logic (math.LO) 03C60 (Primary) 03C98 12J25 14E18 14G20 32P05 32S60 11D88 (Secondary) Analysis Mathematics |
| Zdroj: | Forum of Mathematics, Pi Forum of Mathematics, Pi, 2022, ⟨10.1017/fmp.2022.6⟩ |
| ISSN: | 2050-5086 |
| DOI: | 10.1017/fmp.2022.6⟩ |
| Popis: | We present a framework for tame geometry on Henselian valued fields which we call Hensel minimality. In the spirit of o-minimality, which is key to real geometry and several diophantine applications, we develop geometric results and applications for Hensel minimal structures that were previously known only under stronger, less axiomatic assumptions. We show existence of t-stratifications in Hensel minimal structures and Taylor approximation results which are key to non-archimedean versions of Pila-Wilkie point counting, Yomdin's parameterization results and to motivic integration. In this first paper we work in equi-characteristic zero; in the sequel paper, we develop the mixed characteristic case and a diophantine application. Comment: 90 pages; changes compared to v2: proof of dimension theory is more self-contained; new section 5.8 about motivic integration |
| Databáze: | OpenAIRE |
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