Duke Mathematical Journal

Sur la non-densité des points entiers

Pascal Autissier

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Résumé

On donne des résultats de non-densité pour les points entiers sur des variétés affines, dans l'esprit de la conjecture de Lang-Vojta. En particulier, soit X une variété projective de dimension d≥2 sur un corps de nombres K (resp., sur C). Soit H la somme de 2d diviseurs amples sur X qui se coupent proprement. On montre que tout ensemble de points quasi-entiers (resp., toute courbe entière) sur X−H est non Zariski-dense.

Abstract

We give nondensity results for integral points on affine varieties, in the spirit of the Lang-Vojta conjecture. In particular, let X be a projective variety of dimension d≥2 over a number field K (resp., over C). Let H be the sum of 2d properly intersecting ample divisors on X. We show that any set of quasi-integral points (resp., any integral curve) on X−H is not Zariski-dense.

Article information

Source
Duke Math. J., Volume 158, Number 1 (2011), 13-27.

Dates
First available in Project Euclid: 3 May 2011

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1304429492

Digital Object Identifier
doi:10.1215/00127094-1276292

Mathematical Reviews number (MathSciNet)
MR2794367

Zentralblatt MATH identifier
1217.14020

Subjects
Primary: 14G25: Global ground fields
Secondary: 11J97: Analogues of methods in Nevanlinna theory (work of Vojta et al.) 11G35: Varieties over global fields [See also 14G25]

Citation

Autissier, Pascal. Sur la non-densité des points entiers. Duke Math. J. 158 (2011), no. 1, 13--27. doi:10.1215/00127094-1276292. https://projecteuclid.org/euclid.dmj/1304429492


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