p-adic Hodge Theory and Applications

PI将继续他的工作在p-adic霍奇理论，特别侧重于应用的算术志村品种。特别是它们的积分模型、算术紧化和模点的结构。这应该最终让人们了解上同调的这些品种和伽罗瓦表示发生在那里。p进霍奇理论是分支数论，旨在研究当地的性质伽罗瓦表示所产生的几何。在过去的30年里，这个问题一直是数论中许多最重要的发展的核心（例如费马大定理的证明）。该项目的目的是使用这些技术来研究一类几何对象的算术-志村品种-这已被证明是特别重要的算术应用。

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.