Prisms and prismatic cohomology
Prisms and prismatic cohomology
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DOI：
10.4007/annals.2022.196.3.5
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发表时间：
2019-05
影响因子：
4.9
通讯作者：
B. Bhatt;P. Scholze
中科院分区：
文献类型：
--
作者：
B. Bhatt;P. Scholze
我们引入棱镜的概念，它可以被视为完美样环概念的“缺陷”。使用棱镜，我们将一个环状位置——棱镜位置——附加到一个$p$进的形式方案上。由此产生的上同调理论专门用于（并且经常改进）最著名的积分上同调理论。作为应用，我们证明了允许沿任意闭子集（不使用进空间）分支的几乎纯定理的改进版本，给出了第二作者猜想的$q$-de Rham上同的无坐标描述，并解决了先前与Morrow合作引入的$p$-进的Tate旋$\mathbf{Z}_p(n)$的消失猜想。
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 $\mathbf{Z}_p(n)$ introduced in previous joint work with Morrow.