Parametrizations in valued fields | Vidéo | Carmin.tv

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Parametrizations in valued fields

By Floris Vermeulen

Appears in collection : Tame Geometry Thematic Month Week 3 / Géométrie modérée Mois thématique semaine 3

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.

Information about the video

Date of recording 11/02/2025
Date of publication 28/02/2025
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20314903
Cite this video Vermeulen, Floris (11/02/2025). Parametrizations in valued fields. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20314903
URL https://dx.doi.org/10.24350/CIRM.V.20314903

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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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