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H 0 The generalized Sato-Tate conjecture

Auteurs : Fité, Francesc (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : This series of three talks is the first part of an introductory course on the generalized Sato-Tate conjecture, made in collaboration with Andrew V. Sutherland at the Winter School "Frobenius distributions on curves", celebrated in Luminy in February 2014. In the first talk, some general background following Serre's works is introduced: equidistribution and its connexion to L-functions, the Sato-Tate group and the Sato-Tate conjecture. In the second talk, we present the Sato-Tate axiomatic, which leads us to some Lie group theoretic classification results. The last part of the talk is devoted to illustrate the methods involved in the proof of this kind of results by considering a concrete example. In the third and final talk, we present Banaszak and Kedlaya's algebraic version of the Sato-Tate conjecture, we describe the notion of Galois type of an abelian variety, and we establish the dictionary between Galois types and Sato-Tate groups of abelian surfaces defined over number fields.
    generalized Sato-Tate conjecture - Sato-Tate group - equidistribution - Sato-Tate axioms - Galois type - Abelian surfaces - endomorphism algebra - Frobenius distributions

    11G10 - Abelian varieties of dimension >1
    11G20 - Curves over finite and local fields
    14G10 - Zeta-functions and related questions
    14K15 - Arithmetic ground fields
    11M50 - Relations with random matrices

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 09/10/14
      Date de captation : 17/02/14
      Collection : Number Theory
      Sous collection : Research School
      Format : quicktime ; audio/x-aac
      Domaine : Number Theory
      Durée : 00:58:51
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2014-02-17_Fite_part1.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes
    Organisateurs de la rencontre : Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, Igor
    Dates : 17/02/14 - 28/02/14
    Année de la rencontre : 2014
    URL Congrès : https://www.chairejeanmorlet.com/1059.html

    Citation Data

    DOI : 10.24350/CIRM.V.18605003
    Cite this video as: Fité, Francesc (2014). The generalized Sato-Tate conjecture.CIRM . Audiovisual resource. doi:10.24350/CIRM.V.18605003
    URI : http://dx.doi.org/10.24350/CIRM.V.18605003

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