Vanishing of local cohomology and set-theoretically Cohen-Macaulay ideals

Abstract

In this paper, first, we generalize a result of Peskine-Szpiro on the relation between the cohomological dimension and projective dimension.Then, we give conditions for the vanishing of local cohomology from local to global and vice versa. Our final goal in the present paper is examining the set-theoretically Cohen-Macaulay ideals to find some cohomological characterization of these kinds of ideals.