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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 )

 Loading the player... 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 applicationsOrganisateurs de la rencontre : Maire, Christian ; Ricotta, GuillaumeDates : 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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