On Shimura curves generated by families of Galois G-covers of curves

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-30 DOI:10.1016/j.aim.2024.109855

Abolfazl Mohajer

引用次数: 0

Abstract

In this paper we prove that there are no families of cyclic $Z_{n}$ -covers of elliptic curves which generate non-compact Shimura (special) curves that lie generically in the Torelli locus $T_{g}$ of abelian varieties with $g \geq 8$ when n has a proper prime factor $p \geq 7$ . This non-existence is also shown for families of $Z_{n}$ -covers of curves of any genus s provided that n has a large enough prime factor p (depending on s). We achieve these results by applying the theory of Higgs bundles and the Viehweg-Zuo characterization of Shimura curves in the moduli space of principally polarized abelian varieties.

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论由曲线的伽罗瓦 G 盖族生成的志村曲线

在本文中，我们证明了不存在椭圆曲线的循环-覆盖族，它们生成的非紧凑的志村（特殊）曲线一般位于有适当质因数的非比利亚变体的托雷利（Torelli）位中。只要有一个足够大的质因数（取决于），这种不存在性也适用于任何种属的曲线的-覆盖族。我们通过应用希格斯束理论和主极化阿贝尔变体模空间中的志村曲线的维韦格-左特性来实现这些结果。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.