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Parametrizations in valued fields
Multi angle
Authors : Vermeulen, Floris (Author of the conference)
CIRM (Publisher )
03C98 - Applications of model theory
11D88 - $p$-adic and power series fields
14G05 - Rational points
CIRM (Publisher )
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Abstract :
In the o-minimal setting, parametrizations of definable sets form a key component of the Pila-Wilkie counting theorem. A similar strategy based on parametrizations was developed by Cluckers-Comte-Loeser and Cluckers-Forey-Loeser to prove an analogue of the Pila-Wilkie theorem for subanalytic sets in p-adic fields. In joint work with R. Cluckers and I. Halupczok, we prove the existence of parametriza- tions for arbitrary definable sets in Hensel minimal fields, leading to a counting theorem in this general context.
Keywords : non-archimedean geometry; rational points of bounded height; Taylor approximation; tame geometry; henselian valued fields; Pila-Wilkie theorem
MSC Codes : Keywords : non-archimedean geometry; rational points of bounded height; Taylor approximation; tame geometry; henselian valued fields; Pila-Wilkie theorem
03C98 - Applications of model theory
11D88 - $p$-adic and power series fields
14G05 - Rational points
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 28/02/2025 Conference Date : 11/02/2025 Subseries : Research talks arXiv category : Logic ; Number Theory Mathematical Area(s) : Logic and Foundations ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:48:57 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-02-13_Vermeulen.mp4 
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Information on the Event
Event Title : Tame Geometry Thematic Month Week 3 / Géométrie modérée Mois thématique semaine 3Event Organizers : Matusinski, Mickael ; Rond, Guillaume ; Servi, Tamara ; Speissegger, Patrick Dates : 10/02/2025 - 14/02/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3269.html
Citation Data
DOI : 10.24350/CIRM.V.20314903Cite this video as: Vermeulen, Floris (2025). Parametrizations in valued fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20314903 URI : http://dx.doi.org/10.24350/CIRM.V.20314903 |
See Also
- [Multi angle] Sharply o-minimal structures and sharp cell decomposition / Author of the conference Zak, Benny.
- [Multi angle] Hensel minimality / Author of the conference Rideau-Kikuchi, Silvain.
- [Multi angle] Definable holomorphic continuations in o-minimal structures / Author of the conference Padgett, Adele.
- [Multi angle] Tame geometry in quantum field theory and gravity / Author of the conference Grimm, Thomas.
Bibliography
- CLUCKERS, Raf, COMTE, Georges, et LOESER, François. Non-Archimedean Yomdin–Gromov parametrizations and points of bounded height. In : Forum of Mathematics, Pi. Cambridge University Press, 2015. p. e5. - http://doi.org/10.1017/fmp.2015.4
- CLUCKERS, Raf, FOREY, Arthur, et LOESER, François. Uniform Yomdin–Gromov parametrizations and points of bounded height in valued fields. Algebra & Number Theory, 2020, vol. 14, no 6, p. 1423-1456. - https://doi.org/10.2140/ant.2020.14.1423
- CLUCKERS, Raf, HALUPCZOK, Immanuel, et RIDEAU-KIKUCHI, Silvain. Hensel minimality I. In : Forum of Mathematics, Pi. Cambridge University Press, 2022. p. e11. - https://doi.org/10.1017/fmp.2022.6
- CLUCKERS, Raf, HALUPCZOK, Immanuel, RIDEAU-KIKUCHI, Silvain, et al. Hensel minimality II: Mixed characteristic and a diophantine application. In : Forum of Mathematics, Sigma. Cambridge University Press, 2023. p. e89. - https://doi.org/10.1017/fms.2023.91
- PILA, Jonathan et WILKIE, Alex James. The rational points of a definable set. Duke Math. J. 2006, vol.133 n°3 p.591 - 616. - https://doi.org/10.1215/S0012-7094-06-13336-7
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