Problème de Lehmer relatif dans un tore : cas des hypersurfaces

Details Problème de Lehmer relatif dans un tore : cas des hypersurfaces Problème de Lehmer relatif dans un tore : cas des hypersurfaces

2005-09-08

arxiv.org/abs/math/0509196v1

Mathematics

Number Theory

Scientific paper

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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