Integral points on moduli schemes

被引：0

作者：

von Kanel, Rafael ^{[1
]}

机构：

[1] Tsinghua Univ, IAS, Beijing, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2025年 / 270卷

基金：

中国国家自然科学基金;

关键词：

Diophantine equations; Heights; Effective; ELLIPTIC-CURVES; ABELIAN-VARIETIES; DIOPHANTINE EQUATIONS; SHAFAREVICH CONJECTURE; FINITENESS THEOREM; LINEAR-EQUATIONS; EXPLICIT BOUNDS; ABC CONJECTURE; GOOD REDUCTION; J-INVARIANT;

D O I：

10.1016/j.jnt.2024.07.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The strategy of combining the method of Faltings (Arakelov, Par & scaron;in, Szpiro) with modularity and Masser-W & uuml;stholz isogeny estimates allows to explicitly bound the height and the number of the solutions of certain Diophantine equations related to integral points on moduli schemes of abelian varieties. In this paper we survey the development and various applications of this strategy. (c) 2024 Published by Elsevier Inc.

引用

页码：167 / 237

页数：71

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