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H 1 Maps between curves and diophantine obstructions

Auteurs : Voloch, José Felipe (Auteur de la Conférence)
CIRM (Editeur )

Résumé : Given two algebraic curves $X$, $Y$ over a finite field we might want to know if there is a rational map from $Y$ to $X$. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as $X(K)$ where $K$ is the function field of $Y$. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to this situation and present some results and conjectures that arise.

Codes MSC :
11G20 - Curves over finite and local fields
11G35 - Varieties over global fields
14G05 - Rational points

 Informations sur la Vidéo Réalisateur : Hennenfent, Guillaume Langue : Anglais Date de publication : 29/06/17 Date de captation : 20/06/17 Collection : Research talks Format : MP4 Durée : 00:52:05 Domaine : Algebraic & Complex Geometry ; Number Theory Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2017-06-20_Voloch.mp4 Informations sur la rencontre Nom du congrès : Arithmetic, geometry, cryptography and coding theory / Arithmétique, géométrie, cryptographie et théorie des codesOrganisteurs Congrès : Aubry, Yves ; Howe, Everett ; Ritzenthaler, ChristopheDates : 19/06/17 - 23/06/17 Année de la rencontre : 2017 URL Congrès : http://conferences.cirm-math.fr/1608.htmlCitation Data DOI : 10.24350/CIRM.V.19186203 Cite this video as: Voloch, José Felipe (2017). Maps between curves and diophantine obstructions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19186203 URI : http://dx.doi.org/10.24350/CIRM.V.19186203

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