Sets with few rational points | Vidéo | Carmin.tv

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Sets with few rational points

By Georges Comte

Appears in collection : Real analytic geometry and trajectories of vector fields / Géométrie analytique réelle et trajectoires de champs de vecteurs

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.

Information about the video

Date of recording 09/06/2015
Date of publication 25/06/2015
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18771903
Cite this video Comte, Georges (09/06/2015). Sets with few rational points. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18771903
URL https://dx.doi.org/10.24350/CIRM.V.18771903

Domain(s)

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

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