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H 1 Brauer-Siegel theorem and analogues for varieties over global fields

Auteurs : Hindry, Marc (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The classical Brauer-Siegel theorem can be seen as one of the first instances of description of asymptotical arithmetic: it states that, for a family of number fields $K_i$, under mild conditions (e.g. bounded degree), the product of the regulator by the class number behaves asymptotically like the square root of the discriminant.
    This can be reformulated as saying that the Brauer-Siegel ratio log($hR$)/ log$\sqrt{D}$ has limit 1.
    Even if some of the fundamental problems like the existence or non-existence of Siegel zeroes remains
    unsolved, several generalisations and analog have been developed: Tsfasman-Vladuts, Kunyavskii-Tsfasman, Lebacque-Zykin, Hindry-Pacheco and lately Griffon. These analogues deal with number fields for which the limit is different from 1 or with elliptic curves and abelian varieties either for a fixed variety and varying field or over a fixed field with a family of varieties.

    Codes MSC :
    11G25 - Varieties over finite and local fields
    14G15 - Finite ground fields

      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 : 00:57:40
      Domaine : Algebraic & Complex Geometry ; Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-06-20_Hindry.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 : 19/06/17 - 23/06/17
    Année de la rencontre : 2017
    URL Congrès : http://conferences.cirm-math.fr/1608.html

    Citation Data

    DOI : 10.24350/CIRM.V.19186103
    Cite this video as: Hindry, Marc (2017). Brauer-Siegel theorem and analogues for varieties over global fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19186103
    URI : http://dx.doi.org/10.24350/CIRM.V.19186103

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