On integral points on surfaces
成果类型：
Article
署名作者：
Corvaja, P; Zannier, U
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2004.160.705
发表日期：
2004
页码：
705-726
关键词：
摘要：
We study the integral points on surfaces by means of a new method, relying on the Schmidt Subspace Theorem. This method was recently introduced in [CZ] for the case of curves, leading to a new proof of Siegel's celebrated theorem that any affine algebraic curve defined over a number field has only finitely many S-integral points, unless it has genus zero and not more than two points at infinity. Here, under certain conditions involving the intersection matrix of the divisors at infinity, we shall conclude that the integral points on a surface all lie on a curve. We shall also give several examples and applications. One of them concerns curves, with a study of the integral points defined over a variable quadratic field; for instance we shall show that an affine curve with at least five points at infinity has at most finitely many such integral points.