On cohomologically complete intersections

An ideal I of a local Gorenstein ring (R,m) is called cohomologically complete intersection whenever for all i≠heightI. Here , 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, in particular in terms of their Bass numbers of , c=heightI. As a main result it is shown that the vanishing for all i≠c is completely encoded in homological properties of , in particular in its Bass numbers.