Integral points of Shimura varieties: An “all or nothing” principle

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-05-06 DOI:10.1016/j.jnt.2025.02.003

Haohao Liu

引用次数: 0

Abstract

For algebraic varieties over number fields, we define a locus that measures the infiniteness of integral points (of chosen integral models). For a Shimura variety S, Lang's conjecture predicts that the locus of S is empty when the level structure is high, and we prove that this locus is either empty or S itself.

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志村变异的积分点：一个“全有或全无”的原则

对于数域上的代数变量，我们定义了一个轨迹来测量积分点（所选积分模型）的无穷性。对于Shimura变量S， Lang的猜想预测了当能级结构高时S的轨迹是空的，我们证明了这个轨迹要么是空的，要么是S本身。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.