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
收藏
页码：18752 / 18780
页数：29
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