Weakly proregular sequence and Čech, local cohomology

Based on paper:

• A note on weakly proregular sequences and local cohomology, arXiv: 2105.07652

Abstract

In this lecture, we introduce weakly proregular sequence by Schenzel, it is introduced to study whether there is an isomorphism between Čech cohomology and local cohomology. In [Sch03], he proved that for the Local cohomology and the Čech cohomology defined by the sequence $\underline{a}=a_1,\dots,a_r$, there is an isomorphism between these cohomologies if and only if $\underline{a}$ is weakly proregular. We give an elementary proof of his theorem without using notions of derived category theory. This seminar is based on preprint (arXiv:2105.07652).

Reference:

• [And22] R. Ando, “A note on weakly proregular sequences”, Moroccan Journal of Algebra and Geometry with Applications, Vol. 1, pp. 98–107 (2022). link
• [Sch03] P. Schenzel (2003) “Proregular sequences, local cohomology, and completion”, Math. Scand., Vol. 92, No. 2, pp. 161–180, DOI: 10.7146/math.scand.a-14399.

Links

• Abstract (in Japanese)
• Slide