Topics in arithmetic geometry

算术几何主题

• 批准号: 1404369
• 负责人: Shou-wu Zhang
• 金额: $ 19万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-15 至 2017-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1404369&HistoricalAwards=false
• 关键词: Topics; arithmetic; geometry

This is a project in a subfield of mathematics known as arithmetic geometry. Many of the questions in the project are motivated by the philosophy that algebraic information can be obtained by geometric methods. Solution to the problems under study in this project will have substantial impact on research in cryptography, theoretical physics, and quantum computing.The investigator will study arithmetical intersection numbers of special cycle on Shimura varieties and their relations to the special values of automorphic of L-series. This work will have applications to the Birch and Swinnerton-Dyer conjecture on abelian varieties and the Beilinson--Bloch conjecture on algebraic cycles.

这是一个数学子场的项目，称为算术几何。 该项目中的许多问题都是由可以通过几何方法获得代数信息的哲学的。 解决该项目中研究的问题的解决方案将对密码学，理论物理学和量子计算的研究产生重大影响。研究者将研究Shimura品种特殊周期的算术交集及其与L系列自动型自动形态特殊价值的关系。这项工作将在阿贝尔（Abelian）品种和贝林森（Beilinson）的桦木和swinnerton-dyer猜想中应用于代数周期。

项目成果

On the averaged Colmez conjecture

关于平均科尔梅兹猜想

• DOI: 10.4007/annals.2018.187.2.4
• 发表时间: 2018
• 期刊: Annals of Mathematics
• 影响因子: 4.9
• 作者: Yuan, Xinyi;Zhang, Shou-Wu
• 通讯作者: Zhang, Shou-Wu