Let be an ideal of a commutative Noetherian (not necessarily local) ring . In the case , we show that the subcategory of -cofinite -modules is Abelian. Using this fact and the technique of way-out functors, we show that, if , or if , or if , then the local cohomology module is -cofinite for every -complex with finitely generated homology modules and every . We further answer Hartshorne’s Question 1.3 in the three aforementioned cases, and we reveal a correlation between his Questions 1.1, 1.2, and 1.3.
"A new outlook on cofiniteness." Kyoto J. Math. 60 (3) 1033 - 1045, September 2020. https://doi.org/10.1215/21562261-2021-0007