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

共 21 条

[1] THE CONE OF EFFECTIVE 3-DIMENSIONAL 1-CYCLES [J].

BENVENISTE, X .

MATHEMATISCHE ANNALEN, 1985, 272 (02) :257-265

[2] EXISTENCE OF MINIMAL MODELS FOR VARIETIES OF LOG GENERAL TYPE [J].

Birkar, Caucher ;

Cascini, Paolo ;

Hacon, Christopher D. ;

McKernan, James .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 23 (02) :405-468

[3]

Castaneda D., 2019, Rational approximations on smooth rational surfaces

[4] Cone theorem via Deligne-Mumford stacks [J].

Chen, Jiun-Cheng ;

Tseng, Hsian-Hua .

MATHEMATISCHE ANNALEN, 2009, 345 (03) :525-545

[5] THE APPROXIMATION TO ALGEBRAIC NUMBERS BY RATIONALS [J].

DYSON, FJ .

ACTA MATHEMATICA, 1947, 79 (04) :225-240

[6]

HINDRY M, 2000, GRAD TEXT M, V201, P1

[7] Rational approximations on toric varieties [J].

Huang, Zhizhong .

ALGEBRA & NUMBER THEORY, 2021, 15 (02) :461-512

[8] Three-fold divisorial contractions to singularities of higher indices [J].

Kawakita, M .

DUKE MATHEMATICAL JOURNAL, 2005, 130 (01) :57-126

[9] ON THE LENGTH OF AN EXTREMAL RATIONAL CURVE [J].

KAWAMATA, Y .

INVENTIONES MATHEMATICAE, 1991, 105 (03) :609-611

[10]

Kollar J, 1998, Cambridge Tracts Math, V134, DOI 10.1017/CBO9780511662560

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