Géométrie, points entiers et courbes entières

Autissier, Pascal

Annales scientifiques de l'École Normale Supérieure, Tome 42 (2009), p. 221-239 / Harvested from Numdam

Résumé

Soit $X$ une variété projective sur un corps de nombres $K$ (resp. sur $\mathbb {C}$). Soit $H$ la somme de « suffisamment de diviseurs positifs » sur $X$. On montre que tout ensemble de points quasi-entiers (resp. toute courbe entière) dans $X-H$ est non Zariski-dense.

Abstract

Let $X$ be a projective variety over a number field $K$ (resp. over $\mathbb {C}$). Let $H$ be the sum of “sufficiently many positive divisors” on $X$. We show that any set of quasi-integral points (resp. any integral curve) in $X-H$ is not Zariski dense.

Détail

Publié le : 2009-01-01

MR 2518077 | Zbl 1173.14016

DOI : https://doi.org/10.24033/asens.2094
Classification:  14G25,  11J97,  11G35
Mots clés: géométrie arithmétique, hauteur, points entiers, approximation diophantienne, hyperbolicité

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