Shimura Varieties and Galois representations

志村簇和伽罗瓦表示

• 批准号: 1301921
• 负责人: Mark Kisin
• 金额: $ 30.5万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1301921&HistoricalAwards=false
• 关键词: Shimura; Varieties; Galois; representations

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.

PI 将继续从事 Shimura 品种的算术和应用方面的工作。目标之一是应用 PI 对这些品种的 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扩展到不良减少的情况。一个可能的应用是关于阿贝尔簇的德拉姆-泰特循环结构的结果。志村簇是一类几何对象，在过去 50 年中在数论的许多进展中发挥了非常重要的作用。它们可以被认为是阿贝尔簇的参数（或模）空间。该项目旨在研究 Shimura 簇的数论性质及其在阿贝尔簇算术中的应用。