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H 1 Arithmetic and algebraic hyperbolicity

Auteurs : Javanpeykar, Ariyan (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have only finitely many solutions in the integers?”. Namely, if the zeroes of such a system define a hyperbolic variety, then this system should have only finitely many integer solutions.
    In this talk I will explain how to verify some of the algebraic, analytic, and arithmetic predictions this conjecture makes. I will present results that are joint work with Ljudmila Kamenova.

    Keywords : rational points; hyperbolicity; algebraic variety; Green-Griffiths-Lang conjecture

    Codes MSC :
    14G05 - Rational points
    14G40 - Arithmetic varieties and schemes; Arakelov theory; heights
    32Q45 - Hyperbolic and Kobayashi hyperbolic manifolds

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 27/02/2019
      Date de captation : 18/02/2019
      Collection : Research talks
      Format : MP4
      Durée : 00:55:23
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-02-18_Javanpeykar.mp4

    Informations sur la rencontre

    Nom de la rencontre : Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletages
    Organisateurs de la rencontre : Brotbek, Damian ; Diverio, Simone ; Gasbarri, Carlo ; Rousseau, Erwan
    Dates : 18/02/2019 - 22/02/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2102.html

    Citation Data

    DOI : 10.24350/CIRM.V.19495103
    Cite this video as: Javanpeykar, Ariyan (2019). Arithmetic and algebraic hyperbolicity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19495103
    URI : http://dx.doi.org/10.24350/CIRM.V.19495103


    Voir aussi

    Bibliographie

    1. Javanpeykar, A., & Kamenova, L. (2019). Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps. - https://arxiv.org/abs/1807.03665

    2. Javanpeykar, A., & Vezzani, A. (2018). Non-archimedean hyperbolicity and applications. - https://arxiv.org/abs/1808.09880

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