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Francesco Amoroso
Small points on a multiplicative group and class number problem
Journal de théorie des nombres de Bordeaux, 19 no. 1 (2007), p. 27-39, doi: 10.5802/jtnb.571
Article PDF | Reviews MR 2332051 | Zbl 1131.11044

Résumé - Abstract

Let $V$ be an algebraic subvariety of a torus ${\mathbb{G}}_m^n\hookrightarrow {\mathbb{P}}^n$ and denote by $V^*$ the complement in $V$ of the Zariski closure of the set of torsion points of $V$. By a theorem of Zhang, $V^*$ is discrete for the metric induced by the normalized height $\hat{h}$. We describe some quantitative versions of this result, close to the conjectural bounds, and we discuss some applications to study of the class group of some number fields.

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