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H 1 Algebraic curves with many rational points over non-prime finite fields

Auteurs : Gekeler, Ernst-Ulrich (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We construct curves over finite fields with properties similar to those of classical elliptic or Drinfeld modular curves (as far as elliptic points, cusps, ramification, ... are concerned), but whose coverings have Galois groups of type $\mathbf{GL}(r)$ over finite rings $(r\ge 3)$ instead of $\mathbf{GL}(2)$. In the case where the finite field is non-prime, there results an abundance of series or towers with a large ratio "number of rational points/genus". The construction relies on higher-rank Drinfeld modular varieties and the supersingular trick and uses mainly rigid- analytic techniques.

    Codes MSC :
    11G09 - Drinfel’d modules; higher-dimensional motives, etc. [See also 14L05]
    11G20 - Curves over finite and local fields
    14G15 - Finite ground fields

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 04/06/15
      Date de captation : 19/05/15
      Collection : Research talks ; Algebraic and Complex Geometry ; Number Theory
      Format : quicktime ; audio/x-aac
      Durée : 01:00:37
      Domaine : Algebraic & Complex Geometry ; Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-05-19_Gekeler.mp4

    Informations sur la rencontre

    Nom de la rencontre : Arithmetics, geometry, cryptography and coding theory / Arithmétique, géométrie, cryptographie et théorie des codes
    Organisateurs de la rencontre : Bassa, Alp ; Couvreur, Alain ; Kohel, David
    Dates : 18/05/15 - 22/05/15
    Année de la rencontre : 2015
    URL Congrès : http://conferences.cirm-math.fr/1193.html

    Citation Data

    DOI : 10.24350/CIRM.V.18766403
    Cite this video as: Gekeler, Ernst-Ulrich (2015). Algebraic curves with many rational points over non-prime finite fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18766403
    URI : http://dx.doi.org/10.24350/CIRM.V.18766403


    Bibliographie

    1. Bassa, A., Beelen, P., Garcia, A., & Stichtenoth, H. (2013). Towers of function fields over non-prime finite fields. - http://arxiv.org/abs/1202.5922

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