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 50 条

[21] Counting rational points of a Grassmannian
Kim, Seungki
MONATSHEFTE FUR MATHEMATIK, 2023, 201 (03): : 825 - 864
[22] Remarks on endomorphisms and rational points
Amerik, E.
Bogomolov, F.
Rovinsky, M.
COMPOSITIO MATHEMATICA, 2011, 147 (06) : 1819 - 1842
[23] Counting rational points of a Grassmannian
Seungki Kim
Monatshefte für Mathematik, 2023, 201 : 825 - 864
[24] Rational points on the unit sphere
Schmutz, Eric
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS, 2008, 6 (03): : 482 - 487
[25] DISTRIBUTION OF RATIONAL POINTS: A SURVEY
Takloo-Bighash, Ramin
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2009, 35 (01) : 1 - 30
[26] Rational points and derived equivalence
Addington, Nicolas
Antieau, Benjamin
Honigs, Katrina
Frei, Sarah
COMPOSITIO MATHEMATICA, 2021, 157 (05) : 1036 - 1050
[27] The distribution of rational points on conics
Heath-brown, D. R.
ACTA ARITHMETICA, 2023, 209 (01) : 91 - 128
[28] Rational points of elliptic surfaces and the topology of cubic-line, cubic-conic-line arrangements
Bannai, Shinzo
Tokunaga, Hiro-O
Yamamoto, Momoko
HOKKAIDO MATHEMATICAL JOURNAL, 2020, 49 (01) : 87 - 108
[29] Number of rational points of elliptic curves
Duris, Viliam
Sumny, Timotej
ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, 2022, 15 (01)
[30] Rational points and cohomology of discriminant varieties
Lehrer, GI
ADVANCES IN MATHEMATICS, 2004, 186 (01) : 229 - 250

← 1 2 3 4 5 →