Arithmetic occult period maps

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-04-08 DOI:10.14231/AG-2020-021

Jeff Achter

引用次数: 3

Abstract

Several natural complex configuration spaces admit surprising uniformizations as arithmetic ball quotients, by identifying each parametrized object with the periods of some auxiliary object. In each case, the theory of canonical models of Shimura varieties gives the ball quotient the structure of a variety over the ring of integers of a cyclotomic field. We show that the (transcendentally-defined) period map actually respects these algebraic structures, and thus that occult period maps are arithmetic. As an intermediate tool, we develop an arithmetic theory of lattice-polarized K3 surfaces.

查看原文本刊更多论文

算术隐期图

通过用辅助对象的周期来识别每个参数化对象，一些自然的复构形空间承认了令人惊讶的算术球商均匀化。在每种情况下，志村变数的正则模型理论给出了分环场整数环上变数的球商结构。我们证明(超越定义的)周期映射实际上尊重这些代数结构，因此隐周期映射是算术的。作为一种中间工具，我们发展了晶格极化K3曲面的算术理论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.