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H 1 Maps between curves and diophantine obstructions

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

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    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

      Langue : Anglais
      Date de publication : 29/06/17
      Date de captation : 20/06/17
      Collection : Research talks ; Algebraic and Complex Geometry ; Number Theory
      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 de la rencontre : Arithmetic, geometry, cryptography and coding theory / Arithmétique, géométrie, cryptographie et théorie des codes
    Organisateurs de la rencontre : Aubry, Yves ; Howe, Everett ; Ritzenthaler, Christophe
    Dates : 19/06/17 - 23/06/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1608.html

    Citation 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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