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arXiv · 2009.11563

About proregular sequences and an application to prisms

Peter Schenzel
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Abstract

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 \v{C}ech 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]}).

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Peter Schenzel. 2020-09-24. About proregular sequences and an application to prisms. https://arxiv.org/abs/2009.11563

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