Problème de Lehmer pour les hypersurfaces de variétés abéliennes de type C.M.
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Publication:4811254
DOI10.4064/AA113-3-5zbMath1115.11309arXivmath/0307095OpenAlexW3098604242MaRDI QIDQ4811254
Publication date: 18 August 2004
Published in: Acta Arithmetica (Search for Journal in Brave)
Abstract: We obtain a lower bound for the normalised height of a non-torsion hypersurface $V$ of a C.M. abelian variety $A$ which is a refinement of a precedent result. This lower bound is optimal in terms of the geometric degree of $V$, up to an absolute power of a ``log (independant of the dimension of $A$). We thus extend the results of F. Amoroso and S. David on the same problem on a multiplicative group $mathbb{G}_m^n$. When $A$ is an elliptic curve and $V=�ar{P}$ is the set of conjugates of a non torsion $�ar{k}$-point, we reobtain the result of M. Laurent on the elliptic Lehmer's problem.
Full work available at URL: https://arxiv.org/abs/math/0307095
Abelian varieties of dimension (> 1) (11G10) Heights (11G50) Complex multiplication and abelian varieties (14K22)
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