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H 1 A new Northcott property for Faltings height

Auteurs : Mocz, Lucia (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The Faltings height is a useful invariant for addressing questions in arithmetic geometry. In his celebrated proof of the Mordell and Shafarevich conjectures, Faltings shows the Faltings height satisfies a certain Northcott property, which allows him to deduce his finiteness statements. In this work we prove a new Northcott property for the Faltings height. Namely we show, assuming the Colmez Conjecture and the Artin Conjecture, that there are finitely many CM abelian varieties of a fixed dimension which have bounded Faltings height. The technique developed uses new tools from integral p-adic Hodge theory to study the variation of Faltings height within an isogeny class of CM abelian varieties. In special cases, we are able to use these techniques to moreover develop new Colmez-type formulas for the Faltings height.

    Codes MSC :
    11G50 - Heights
    11R04 - Algebraic numbers; rings of algebraic integers
    12F05 - Algebraic extensions
    14G40 - Arithmetic varieties and schemes; Arakelov theory; heights

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 30/05/2018
      Date de captation : 22/05/2018
      Collection : Research talks ; Algebraic and Complex Geometry ; Number Theory
      Format : MP4
      Durée : 00:55:55
      Domaine : Algebraic & Complex Geometry ; Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2018-05-22_Mocz.mp4

    Informations sur la rencontre

    Nom de la rencontre : Diophantine geometry / ​Géométrie diophantienne
    Organisateurs de la rencontre : Bosser, Vincent ; Carrizosa, Maria ; Gaudron, Eric ; Habegger, Philipp
    Dates : 21/05/2018 - 25/05/2018
    Année de la rencontre : 2018
    URL Congrès : https://conferences.cirm-math.fr/1754.html

    Citation Data

    DOI : 10.24350/CIRM.V.19407903
    Cite this video as: Mocz, Lucia (2018). A new Northcott property for Faltings height. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19407903
    URI : http://dx.doi.org/10.24350/CIRM.V.19407903


    Voir aussi

    Bibliographie

    1. Mocz, L. (2017). A new Northcott property for Faltings height. - https://arxiv.org/abs/1709.06098

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