About proregular sequences and an application to prisms

2020/09/24 by Schenzel, Peter
#13C11 #13C12 #13D07 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.11563

Abstract

Let \underlinex = x₁,…,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 \underlinex 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 \underlinex to be M-proregular in terms of Čech homology. This implies also that \underlinex 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]).

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