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Problème de Lehmer relatif dans un tore : cas des hypersurfaces

Emmanuel Delsinne
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Abstract

We tackle the "relative" Lehmer problem on algebraic subvarieties of a multiplicative torus. Generalizing a theorem of F. Amoroso and U. Zannier, we give a lower bound for the normalized height of a non torsion hypersurface in terms of its obstruction index over $\Q^{ab}$, the maximal abelian extension of $\Q$. We prove up to $\eps$ the sharpest conjecture that can be formulated.

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Emmanuel Delsinne. 2005-09-08. Problème de Lehmer relatif dans un tore : cas des hypersurfaces. https://arxiv.org/abs/math/0509196

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