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Sets with few rational points
Multi angle
Authors : Comte, Georges (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 spirit of famous papers by Pila & Bombieri and Pila & Wilkie, I will explain how to bound the number of rational points, with respect to their height, in various kinds of sets, such as transcendental sets definable in some o-minimal - or even not o-minimal - structure over the real field. I will emphazise the role played by bounds on derivatives and on sets of zeroes in this context.
MSC Codes : 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 : 25/06/15 Conference Date : 09/06/15 Subseries : Research talks arXiv category : Algebraic Geometry ; Number Theory ; Logic in Computer Science Mathematical Area(s) : Logic and Foundations ; Number Theory ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:45:33 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-06-09_Comte.mp4 
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Information on the Event
Event Title : Real analytic geometry and trajectories of vector fields / Géométrie analytique réelle et trajectoires de champs de vecteurs Event Organizers : Kurdyka, Krzysztof ; Parusinski, Adam ; Rolin, Jean-Philippe ; Sanz, Fernando Dates : 08/06/15 - 12/06/15 Event Year : 2015 Event URL : http://conferences.cirm-math.fr/1220.html
Citation Data
DOI : 10.24350/CIRM.V.18771903Cite this video as: Comte, Georges (2015). Sets with few rational points. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18771903 URI : http://dx.doi.org/10.24350/CIRM.V.18771903 |
Bibliography
- Pila, J., & Wilkie, A.J.(2006). The rational points of a definable set. Duke Mathematical Journal, 133(3), 591-616 - http://dx.doi.org/10.1215/S0012-7094-06-13336-7
