棱镜晶体层的上同调

Cohomology of Prismatic Crystals

本文是一篇关于棱镜上同调理论发展的论文综述.我们将从经典的p-进制Hodge理论开始,简要地综述棱镜上同调理论的起源和基本结果.我们将重点介绍棱镜晶体层的概念,它们的上同调基本性质,以及它们与经典的晶体上同调的关系.

This article is a survey on some recent developement of the prismatic cohomology theory.We will start with some motivation from classical p-adic Hodge theory,and discuss the origine of the prismatic cohomolgy theory and its basic results.We will then put emphasis on the notion of prismatic crystals,their cohomological properties,and the relationship with the cohomology of classical crystalline crystals.