A note on weakly proregular sequence
Published in Moroccan Journal of Algebra and Geometry with Applications, April 2022. Links: journal, arXiv:
Citation: R. Ando, A note on weakly proregular sequence, Moroccan Journal of Algebra and Geometry with Applications, Vol. 1, pp. 98--107 (2022)
Comment
In this paper, we give an elementary proof of the result given by Schenzel that there are functorial iso- morphisms between local cohomology groups and ˇCech 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 Schenzel’s paper, 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.