论文标题
关于牙齿序列和棱镜的应用
About proregular sequences and an application to prisms
论文作者
论文摘要
令$ \ usewandline {x} = x_1，\ ldots，x_k $表示通勤环$ r $的元素的有序序列。令$ m $为$ r $ - 模块。我们回想起$ \ upessline {x} $是$ m $ - 前提是Greenlees和May（见\ cite {[5]}）和Lipman（见\ cite {[1]}），并表明这两个概念都是等量的。作为主要结果，我们证明了$ \ usepline {x} $的共同体表征，就$ m $ - 前牙性而言。这也意味着$ \ useverline {x} $是$ m $ - 呈$ m $ - $ m $ - 前牙。证明了局部全球性原则和弱质观。这用于关于Bhatt和Scholze引入的棱镜的结果（见\ cite {[3]}）。
Let $\underline{x} = x_1,\ldots,x_k$ denote an ordered sequence of elements of a commutative ring $R$. Let $M$ be an $R$-module. We recall the two notions that $\underline{x}$ is $M$-proregular given by Greenlees and May (see \cite{[5]}) and Lipman (see \cite{[1]}) and show that both notions are equivalent. As a main result we prove a cohomological characterization for $\underline{x}$ to be $M$-proregular in terms of Čech homology. This implies also that $\underline{x}$ is $M$-weakly proregular if it is $M$-proregular. A local-global principle for proregularity and weakly proregularity is proved. This is used for a result about prisms as introduced by Bhatt and Scholze (see \cite{[3]}).
