About proregular sequences and an application to prisms. Issue 11 (3rd November 2021) - Schenzel, Peter
Abstract: Let x ¯ = x 1, …, 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 x ¯ 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 x ¯ to be M -proregular in terms of Čech cohomology. This implies also that 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.