p-adic Hodge Theory and Applications

p-进霍奇理论及其应用

• 批准号: 1001139
• 负责人: Mark Kisin
• 金额: $ 39万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1001139&HistoricalAwards=false
• 关键词: adic; Hodge; Theory; Applications

The PI will continue his work in p-adic Hodge theory, with a particular focus on applications to the arithmetic of Shimura varieties. In particular, their integral models, arithmetic compactifications and the structure of their mod p points. This should eventually allow one to understand the cohomology of these varieties and the Galois representations which occur there.p-adic Hodge theory is branch of number theory which seeks to study the local properties of Galois representations which arise from geometry. The subject has been at the heart of many of the most important developments in number theory in the last 30 years (e.g the proof of Fermat's Last theorem). The project aims to use these techniques to study the arithmetic of a class of geometric objects - Shimura varieties - which have proved particularly important in arithmetic applications.

PI 将继续他在 p 进 Hodge 理论方面的工作，特别关注 Shimura 簇算术的应用。特别是它们的积分模型、算术压缩及其 mod p 点的结构。这最终应该使人们能够理解这些簇的上同调以及其中出现的伽罗瓦表示。 p-adic Hodge 理论是数论的一个分支，旨在研究源自几何的伽罗瓦表示的局部性质。该主题一直是过去 30 年来数论许多最重要发展的核心（例如费马大定理的证明）。该项目旨在利用这些技术来研究一类几何对象（志村变体）的算术，这已被证明在算术应用中特别重要。