Shimura Varieties and Galois representations

PI将继续他在下村变种和应用的算术方面的工作。一个目标是应用PI关于这些变种的mod p点的最新结果来计算它们的zeta函数。另一个目标是将其中一些结果推广到复位不良的情况。一个可能的应用是关于阿贝尔簇上的De Rham-Tate圈的结构的结果。Shimura簇是一类几何对象，在过去50年的许多数论进步中发挥了非常重要的作用。它们可以被认为是交换簇的参数(或模)空间。本项目旨在研究Shimura变种的数论性质及其在交换变种算法中的应用。

The PI will continue his work on the arithmetic of Shimura varieties and applications. One goal is to apply the PI's recent results on the mod p points on these varieties to compute their zeta functions. Another aim is to extend some of these results to cases of bad reduction. One possible application is a result about the structure of de Rham-Tate cycles on abelian varieties.Shimura varieties are a class of geometric objects which have played a very important role in many advances in number theory during the past 50 years. They can be thought of as parameter (or moduli) spaces for abelian varieties. The project aims to study the number theoretic properties of Shimura varieties, and their applications to the arithmetic of abelian varieties.