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Theses

Minoration de la hauteur de Néron-Tate sur les variétés abéliennes : sur la conjecture de Lang et Silverman.

Abstract : This thesis concentrates on a conjecture made by Lang and Silverman which gives a uniform lower bound for the Néron-Tate height on abelian varieties over number fields. The first chapter provides a background for the understanding of the following chapters and fixes the notations and normalisations used throughout the text. It is proven in the second chapter that the conjecture is true for some classes of abelian surfaces, in particular jacobians with potentially good reduction that lie outside an "epsilon-neighbourhood" of the elliptic curve product locus. This chapter also includes statements towards the uniform torsion bound conjecture and uniform bounds on the number of rational points on curves of genus 2. The third chapter generalizes the previous bounds for heights to jacobians of hyperelliptic curves of greater genus. The fourth chapter studies the restriction of scalars à la Weil and gives an asymptotic result for the height of Heegner points on jacobians of modular curves. The fifth chapter includes explicit formulas useful in dimension 2 and a short study involving isogenies.
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https://tel.archives-ouvertes.fr/tel-00419059
Contributor : Fabien Pazuki <>
Submitted on : Tuesday, September 22, 2009 - 3:26:08 PM
Last modification on : Wednesday, November 29, 2017 - 2:56:59 PM
Long-term archiving on: : Tuesday, June 15, 2010 - 11:59:50 PM

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  • HAL Id : tel-00419059, version 1

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Fabien Pazuki. Minoration de la hauteur de Néron-Tate sur les variétés abéliennes : sur la conjecture de Lang et Silverman.. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2008. Français. ⟨tel-00419059⟩

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