2013/12/25 by Waqas Mahmood, Mahmood, Waqas
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.1312.6961
16 pages, submitted. arXiv admin note: text overlap with arXiv:0804.2558 by other authors
arxiv created 2014/01/01 · arxiv updated 2014/01/03
An ideal I of a local Cohen-Macaulay ring R is called a cohomologically complete intersection if HiI(R) = 0 for all i ≠ c = height(I). Here HiI(R), i ∈ 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 HiI_(M) = 0 for all i ≠ c is completely encoded in homological properties of HcI_(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.