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Pré-Publication, Document De Travail Année : 2004

Deux remarques sur le probleme de Lehmer sur les varietes abeliennes

Résumé

Let $A/K$ be an abelian variety over a number field $K$. We prove in this article that a good lower bound (in terms of the degree $[K(P):K]$) for the Néron-Tate height of the points $P$ of infinite order modulo every strict abelian subvarieties of $A$ implies a good lower bound for the height of all the non-torsion points of $A$. In particular when $A$ is of C.M. type, a theorem of David and Hindry enables us to deduce, up to ``log'' factors, an optimal lower bound for the height of the non-torsion points of $A$. In the C.M. type case, this improves the previous result of Masser \cite{lettre}. Using the same theorem of David and Hindry we prove in the second part an optimal lower bound, up to ``log'' factors, for the product of the Néron-Tate height of $n$ End$(A)$-linearly independant non-torsion points of a C.M. type abelian variety.

Dates et versions

hal-00122370 , version 1 (30-12-2006)

Identifiants

Citer

Nicolas Ratazzi. Deux remarques sur le probleme de Lehmer sur les varietes abeliennes. 2004. ⟨hal-00122370⟩
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