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Multi angle Local densities compute isogeny classes

Auteurs : Achter, Jeffrey (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Consider an ordinary isogeny class of elliptic curves over a finite, prime field. Inspired by a random matrix heuristic (which is so strong it's false), Gekeler defines a local factor for each rational prime. Using the analytic class number formula, he shows that the associated infinite product computes the size of the isogeny class.
    I'll explain a transparent proof of this formula; it turns out that this product actually computes an adelic orbital integral which visibly counts the desired cardinality. Moreover, the new perspective allows a natural generalization to higher-dimensional abelian varieties. This is joint work with Julia Gordon and S. Ali Altug.

    Codes MSC :
    11G20 - Curves over finite and local fields
    14G15 - Finite ground fields
    22E35 - Analysis on $p$-adic Lie groups

    Ressources complémentaires :
    http://www.cirm-math.fr/ProgWeebly/Renc1608/achter.pdf

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 29/06/17
      Date de captation : 22/06/17
      Collection : Research talks
      Format : MP4
      Durée : 00:29:31
      Domaine : Algebraic & Complex Geometry ; Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : http://videos.cirm-math.fr/2017-06-22_Achter.mp4

    Informations sur la rencontre

    Nom du congrès : Arithmetic, geometry, cryptography and coding theory / Arithmétique, géométrie, cryptographie et théorie des codes
    Organisteurs Congrès : Aubry, Yves ; Howe, Everett ; Ritzenthaler, Christophe
    Dates : 19/06/2017 - 23/06/2017
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1608.html

    Citation Data

    DOI : 10.24350/CIRM.V.19186303
    Cite this video as: Achter, Jeffrey (2017). Local densities compute isogeny classes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19186303
    URI : http://dx.doi.org/10.24350/CIRM.V.19186303


    Voir aussi

    Bibliographie

    1. Achter, J.D., & Gordon, J. (2017). Elliptic curves, random matrices and orbital integrals. Pacific Journal of Mathematics, 286(1), 1-24 - http://dx.doi.org/10.2140/pjm.2017.286.1

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