A note on weakly proregular sequence
Ryoya Ando
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science 2641
Yamazaki, Noda-shi, Chiba-ken, 278-8510, Japan.
Pages 98-107 | Received 04 August 2021, Accepted 11 October 2021, Published 01 June 2022
Abstract
In this paper, we give an elementary proof of the result given by Schenzel that there are functorial isomorphisms between local cohomology groups and Čech cohomology groups, by using weakly proregular sequences. The existence of these isomorphisms was well-known for Noetherian rings, but he generalised it to non-Noetherian rings and gave necessary and sufficient conditions for cohomology to coincide. In [6], he used notions of derived category theory in his proof, but we do not use them in this paper. We give a proof within Abelian category theory.
Keywords: Weakly proregular sequence, local cohomology, Čech cohomology.
MSC numbers: Primary 13D03; Secondary 13D45.
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