Topics in arithmetic algebraic geometry

算术代数几何专题

• 批准号: 0970100
• 负责人: Shou-wu Zhang
• 金额: $ 30万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0970100&HistoricalAwards=false
• 关键词: Topics; arithmetic; algebraic; geometry

The investigator and his collabortaors and students study several topics in arithmetic geometry, in particular to arithmetical intersection theory of cycle on Shimura varieties with connection to special values of automorphic of L-series extending his previous work on the Gross-Zagier formula and Arakelov theory.This is a project in a subfield of mathematics known as number theory. Many of these questions are motivated by the philosophy that algebraic informations can be obtained by geometric methods. It is not too ambitious to say that the solution to the problems in this proposal will one day affect research in cryptography, theoretic physics, and quantum computing.

研究者和他的合作者和学生研究了算术几何中的几个主题，特别是与l系列自同构的特殊值有关的Shimura变上的循环的算术相交理论，扩展了他之前在Gross-Zagier公式和Arakelov理论方面的工作。这是数学分支数论的一个项目。许多这样的问题是由这样一种哲学所激发的：代数信息可以通过几何方法获得。可以毫不夸张地说，本提案中问题的解决方案有一天会影响密码学、理论物理和量子计算的研究。