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Manuscripta Mathematica

, Volume 142, Issue 1–2, pp 61–99 | Cite as

Minoration de la hauteur de Néron-Tate sur les surfaces abéliennes

  • Fabien PazukiEmail author
Article

Abstract

This paper contains results concerning a conjecture made by Lang and Silverman, predicting a lower bound for the canonical height on abelian varieties of dimension 2 over number fields. The method used here is a local height decomposition. We derive as corollaries uniform bounds on the number of torsion points on families of abelian surfaces and on the number of rational points on families of genus 2 curves.

Mathematics Subject Classification

11G50 14G40 14G05 11G30 11G10 

Résumé

On obtient dans le présent texte des résultats en direction d’une conjecture de Lang et Silverman de minoration de la hauteur canonique sur les variétés abéliennes de dimension 2 sur un corps de nombres. La méthode utilisée est une décomposition en hauteurs locales. On déduit en corollaire une borne uniforme sur la torsion de familles de surfaces abéliennes et une borne uniforme sur le nombre de points rationnels de familles de courbes de genre 2.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Théorie des nombres, IMB Université Bordeaux 1Talence CedexFrance

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