Géométrie, points entiers et courbes entières

Autissier, Pascal

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 42 (2009) no. 2, pp. 221-239.

Soit $X$ une variété projective sur un corps de nombres $K$ (resp. sur $ℂ$). 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.

Let $X$ be a projective variety over a number field $K$ (resp. over $ℂ$). 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.

Classification : 14G25, 11J97, 11G35
Mot clés : géométrie arithmétique, hauteur, points entiers, approximation diophantienne, hyperbolicité
Keywords: arithmetic geometry, height, integral points, diophantine approximation, hyperbolicity

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