Linear and Quadratic Chabauty for Affine Hyperbolic Curves

被引：0

作者：

Leonhardt, Marius ^{[1
]}

Luedtke, Martin ^{[2
]}

Mueller, J. Steffen ^{[2
]}

机构：

[1] Heidelberg Univ, Math Inst, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

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

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2023年 / 2023卷 / 21期

关键词：

RATIONAL-POINTS;

D O I：

10.1093/imrn/rnad185

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give sufficient conditions for finiteness of linear and quadratic refined Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing depth quotients of the fundamental group, following a construction of Balakrishnan-Dogra in the projective case. We also apply Betts' machinery of weight filtrations to give unconditional explicit upper bounds on the number of -integral points when our conditions are satisfied.

引用

页码：18752 / 18780

页数：29

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