Communications in Algebra ( IF 0.6 ) Pub Date : 2021-06-12 , DOI: 10.1080/00927872.2021.1927067 Peter Schenzel 1
Abstract
Let denote an ordered sequence of elements of a commutative ring R. Let M be an R-module. We recall the two notions that is M-proregular given by Greenlees and May and Lipman and show that both notions are equivalent. As a main result we prove a cohomological characterization for to be M-proregular in terms of Čech cohomology. This implies also that 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.
中文翻译:
关于正则序列和棱镜的应用
摘要
让 表示交换环R的有序元素序列。令M为R模。我们记得这两个概念是M -proregular 由格林利斯和梅和利普曼给出,并表明这两个概念是等价的。作为主要结果,我们证明了在 Čech 上同调方面是M -proregular。这也意味着是中号-weakly proregular如果是中号-proregular。证明了前正则性和弱前正则性的局部全局原理。这用于 Bhatt 和 Scholze 介绍的关于棱镜的结果。