Dokument: Hensel minimality I
| Titel: | Hensel minimality I | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=71469 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20251121-125416-1 | |||||||
| Kollektion: | Publikationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Texte » Artikel, Aufsatz | |||||||
| Medientyp: | Text | |||||||
| Autoren: | Halupczok, Immanuel [Autor] Cluckers, Raf [Autor] Rideau-Kikuchi, Silvain [Autor] | |||||||
| Dateien: |
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| Stichwörter: | Taylor approximation , Non-Archimedean geometry , quantifier elimination , Lipschitz continuity , tame geometry on Henselian valued fields , cell decomposition , analogues to o-minimality | |||||||
| Beschreibung: | 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 the existence of t-stratifications in Hensel minimal structures and Taylor approximation results that are key to non-Archimedean versions of Pila–Wilkie point counting, Yomdin’s parameterization results and 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. | |||||||
| Rechtliche Vermerke: | Originalveröffentlichung:
Cluckers, R., Halupczok, I., & Rideau-Kikuchi, S. (2022). Hensel minimality I. Forum of Mathematics. Pi, 10, Article e11. https://doi.org/10.1017/fmp.2022.6 | |||||||
| Lizenz: |  Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät | |||||||
| Dokument erstellt am: | 21.11.2025 | |||||||
| Dateien geändert am: | 21.11.2025 |
