模态方案上的积分点

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-08-30 DOI:10.1016/j.jnt.2024.07.005

Rafael von Känel

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引用次数: 0

摘要

将法尔廷斯方法（Arakelov, Paršin, Szpiro）与模块性和马塞尔-伍斯特霍尔茨同源估计相结合的策略，可以明确约束与无常变体模态上积分点有关的某些二叉方程的解的高度和数目。在本文中，我们将考察这一策略的发展和各种应用。

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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Integral points on moduli schemes

The strategy of combining the method of Faltings (Arakelov, Paršin, Szpiro) with modularity and Masser–Wüstholz 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.

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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.