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

共 50 条

[31] ON THE LINEAR-TYPE PROPERTY OF THE JACOBIAN IDEAL OF AFFINE PLANE CURVES
Nejad, Abbas Nasrollah
Solhi, Parisa
[J]. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2024, 54 (03) : 843 - 853
[32] HYPERBOLIC TESSELLATIONS, MODULAR SYMBOLS, AND ELLIPTIC-CURVES OVER COMPLEX QUADRATIC FIELDS
CREMONA, JE
[J]. COMPOSITIO MATHEMATICA, 1984, 51 (03) : 275 - 323
[33] Cubic and Quartic Points on Modular Curves Using Generalised Symmetric Chabauty
Box, Josha
Gajovic, Stevan
Goodman, Pip
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (07) : 5604 - 5659
[34] Uniqueness conditions for the affine open-loop linear quadratic differential game
Engwerda, Jacob
[J]. AUTOMATICA, 2008, 44 (02) : 504 - 511
[35] Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties
Balakrishnan, Jennifer S.
Dogra, Netan
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021, 2021 (15) : 11923 - 12008
[36] QUADRATIC HYPERBOLIC OPERATORS
HORMANDER, L
[J]. LECTURE NOTES IN MATHEMATICS, 1991, 1495 : 118 - 160
[37] Affine monomial curves
Indranath Sengupta
[J]. Proceedings - Mathematical Sciences, 2022, 132
[38] Affine monomial curves
Sengupta, Indranath
[J]. PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2022, 132 (01):
[39] ON THE CURVES WITH AFFINE CONGRUENT ARCS IN AFFINE SPACE
Polikanova, Irina Viktorovna
[J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 : 1612 - 1622
[40] Linear and quadratic least squares finite element method for the solution of hyperbolic problems
Afshar, MH
Morgan, K
[J]. ADVANCES IN FLUID MECHANICS II, 1998, 21 : 93 - 101

← 1 2 3 4 5 →