About proregular sequences and an application to prisms. Issue 11 (3rd November 2021)

• Record Type: Journal Article
• Authors: Schenzel, Peter
• Is Part Of: Communications in algebra. Volume 49:Issue 11(2021)
• Page Start: 4687
• Page End: 4698
• Publication Date: 2021-11-03
• Subjects: Injective module -- non-Noetherian commutative ring -- proregular sequences -- torsion; Primary: 13C12 -- Secondary: 13C11 -- 13D07; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2021.1927067
• Languages: English
• ISSNs: 0092-7872

Abstract

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.