A note on weakly proregular sequences

Comment

In this paper, we give an elementary proof of Schenzel’s theorem comparing local cohomology and Čech cohomology in terms of weakly proregular sequences. Such functorial isomorphisms were well known for Noetherian rings; Schenzel extended this to the non-Noetherian setting and gave necessary and sufficient conditions for the two theories to agree. In Schenzel’s paper, the argument uses derived categories; our proof stays within Abelian category theory.