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H 1 Bounds for the number of rational points on curves over global fields

Auteurs : Pazuki, Fabien (Auteur de la Conférence)
CIRM (Editeur )

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curve Mordell's conjecture Faltings Samuel Grauert rank one big rank isotrivial Jacobian theta Rémond Lang Silverman Euclidian function field Pacheco Pazuki Buium Voloch Conceçao Ulmer Voloch rational points Stoll rational points genus 2 rational points conductor

Résumé : Rational points on smooth projective curves of genus $g \ge 2$ over number fields are in finite number thanks to a theorem of Faltings from 1983. The same result was known over function fields of positive characteristic since 1966 thanks to a theorem of Samuel. The aim of the talk is to give a bound as uniform as possible on this number for curves defined over such fields. In a first part we will report on a result by Rémond concerning the number field case and on a way to strengthen it assuming a height conjecture. During the second part we will focus on function fields of positive characteristic and describe a new result obtained in a joined work with Pacheco.

Codes MSC :
11G35 - Varieties over global fields
14G05 - Rational points

    Informations sur la Vidéo

    Langue : Anglais;Français
    Date de publication : 28/04/14
    Date de captation : 12/03/14
    Collection : Research talks ; Algebra ; Number Theory
    Format : QuickTime (.mov) Durée : 00:53:57
    Domaine : Algebra ; Number Theory
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2014-03-12_Pazuki.mp4

Informations sur la rencontre

Nom de la rencontre : Number theory and applications / Théorie des nombres et applications
Organisateurs de la rencontre : Maire, Christian ; Ricotta, Guillaume
Dates : 10/03/14 - 14/03/14
Année de la rencontre : 2014

Citation Data

DOI : 10.24350/CIRM.V.18477603
Cite this video as: Pazuki, Fabien (2014). Bounds for the number of rational points on curves over global fields. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18477603
URI : http://dx.doi.org/10.24350/CIRM.V.18477603


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