On Cohomologically Complete Intersections in Cohen-Macaulay Rings
Abstract
An ideal I of a local Cohen-Macaulay ring R is called a cohomologically complete intersection if H^i_I(R) = 0 for all i \neq c = height(I). Here H^i_I(R), i \in Z denotes the local cohomology of R with respect to I. For instance, a set-theoretic complete intersection is a cohomologically complete intersection. Here we study cohomologically complete intersections from various homological points of view. As a main result it is shown that the vanishing H^iI_(M) = 0 for all i \neq c is completely encoded in homological properties of H^cI_(M). These results extend those of Hellus and Schenzel (see [13, Theorem 0.1]) shown in the case of a local Gorenstein ring. In particular we get a characterization of cohomologically complete intersections in a Cohen-Macaulay ring in terms of the canonical module.
Cite
@article{arxiv.1312.6961,
title = {On Cohomologically Complete Intersections in Cohen-Macaulay Rings},
author = {Waqas Mahmood},
journal= {arXiv preprint arXiv:1312.6961},
year = {2014}
}
Comments
16 pages, submitted. arXiv admin note: text overlap with arXiv:0804.2558 by other authors