A note on weakly proregular sequences and local cohomology

TL;DR

This paper provides an elementary proof of the isomorphism between local cohomology and Čech cohomology using weakly proregular sequences, avoiding the derived category theory used in previous proofs.

Contribution

It offers a simpler, more accessible proof of a known isomorphism by employing weakly proregular sequences instead of derived category methods.

Findings

Established functorial isomorphisms between local and Čech cohomology

Simplified proof avoiding derived category theory

Enhanced understanding of weakly proregular sequences' role

Abstract

In this note, we give an elementary proof of the result given by Schenzel that there are functorial isomorphisms between local cohomology groups and \v{C}ech cohomology groups, by using weakly proregular sequences. In [Sch03], he used notions of derived category theory in his proof, but we do not use them in this paper.