Refined Chabauty-Kim computations for the thrice-punctured line over Z[1/6]

被引：0

作者：

Ludtke, Martin ^{[1
]}

机构：

[1] Univ Groningen, Bernoulli Inst, Nijenborgh 9, NL-9747 AG Groningen, Netherlands

来源：

RESEARCH IN NUMBER THEORY | 2025年 / 11卷 / 01期

关键词：

MIXED TATE MOTIVES;

D O I：

10.1007/s40993-024-00597-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Chabauty-Kim method and its refined variant by Betts and Dogra aim to cut out the S-integral points X(Z(S)) on a curve inside the p-adic points X(Z(p)) by producing enough Coleman functions vanishing on them. We derive new functions in the case of the thrice-punctured line when S contains two primes. We describe an algorithm for computing refined Chabauty-Kim loci and verify Kim's Conjecture over Z[1/6] for all choices of auxiliary prime p<10,000.

引用

页数：22

共 3 条

[1] Explicit Chabauty-Kim theory for the thrice punctured line in depth 2
Dan-Cohen, Ishai
Wewers, Stefan
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 110 : 133 - 171
[2] REFINED SELMER EQUATIONS FOR THE THRICE-PUNCTURED LINE IN DEPTH TWO
Best, Alex J.
Betts, Alexander
Kumpitsch, Theresa
Ludtke, Martin
Mcandrew, Angus W.
Qian, Lie
Studnia, Elie
Xu, Yujie
MATHEMATICS OF COMPUTATION, 2024, 93 (347) : 1497 - 1527
[3] Refined Chabauty–Kim computations for the thrice-punctured line over Z[1/6]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {Z}[1/6]$$\end{document}
Martin Lüdtke
Research in Number Theory, 2025, 11 (1)

← 1 →