Prisms and prismatic cohomology
成果类型：
Article
署名作者：
Bhatt, Bhargav; Scholze, Peter
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2022.196.3.5
发表日期：
2022
页码：
1135-1275
关键词：
摘要：
We introduce the notion of a prism, which may be regarded as a deperfection of the notion of a perfectoid ring. Using prisms, we attach a ringed site - the prismatic site - to a p-adic formal scheme. The resulting cohomology theory specializes to (and often refines) most known integral p-adic cohomology theories. As applications, we prove an improved version of the almost purity theorem allowing ramification along arbitrary closed subsets (without using adic spaces), give a co-ordinate free description of q-de Rham cohomology as conjectured by the second author, and settle a vanishing conjecture for the p-adic Tate twists Zp(n) introduced in our previous joint work with Morrow.