APPROXIMATING RATIONAL POINTS ON SURFACES

被引：0

作者：

Lehmann, Brian ^{[1
]}

Mckinnon, David ^{[2
]}

Satriano, Matthew ^{[2
]}

机构：

[1] Boston Coll, Dept Math, Fifth Floor,Maloney Hall, Chestnut Hill, MA 02467 USA

[2] Univ Waterloo, Dept Pure Math, Waterloo, ON N2L 3G1, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2025年 / 153卷 / 05期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Coba conjecture; Diophantine geometry; rational points; Vojta's conjecture;

D O I：

10.1090/proc/17131

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let X be a smooth projective algebraic variety over a number field k and P is an element of X(k). McKinnon [J. Algebraic Geom. 16 (2007), pp. 257-303] conjectured that, in a precise sense, if rational points on X are dense enough, then the best rational approximations to P must lie on a curve. We present a strategy for deducing a slightly weaker conjecture from Vojta's conjecture, and execute the strategy for the full conjecture for split surfaces.

引用

页码：1903 / 1915

页数：13

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