Topics in arithmetic geometry

这是数学的一个分支——算术几何的一个项目。项目中的许多问题都是由代数信息可以通过几何方法获得的理念所激发的。本项目所研究问题的解决方案将对密码学、理论物理和量子计算的研究产生重大影响。本文将研究Shimura变量上特殊循环的算术交数及其与l系列自同构特殊值的关系。这项工作将应用于关于阿贝尔变的Birch和Swinnerton-Dyer猜想以及关于代数循环的Beilinson- Bloch猜想。

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.