Integral Points on Varieties With Infinite etale Fundamental Group

被引：0

作者：

Achenjang, Niven T. ^{[1
]}

Morrow, Jackson S. ^{[2
]}

机构：

[1] MIT, Dept Math, Cambridge, MA 02139 USA

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2024年 / 2024卷 / 10期

关键词：

APPROXIMATION; SUBVARIETIES; COMPLEMENT;

D O I：

10.1093/imrn/rnad147

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study integral points on varieties with infinite etale fundamental groups. More precisely, for a number field F and X/F a smooth projective variety, we prove that for any geometrically Galois cover phi : Y -> X of degree at least 2 dim(X)(2), there exists an ample line bundle L on Y such that for a general member D of the complete linear system |L|, D is geometrically irreducible and any set of phi (D)-integral points on X is finite. We apply this result to varieties with infinite etale fundamental group to give new examples of irreducible, ample divisors on varieties for which finiteness of integral points is provable.

引用

页码：8157 / 8171

页数：15

共 25 条

[1] REGARDING THE NON-DENSITY OF INTEGRAL POINTS [J].