On cohomologically complete intersections

An ideal $I$ of a local Gorenstein ring $(R,\mathfrak{m})$ is called cohomologically complete intersection whenever $H_I^i(R)=0$ for all $i \not= \height I.$Here$H^i_I®, i \in \mathbb Z,$denotesthelocalcohomologyof$R$withrespectto$I.$ 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 $H_I^c(R),c=\text{height}I\mathrm{.}$ As a main result it is shown that the vanishing $H_I^i(R)=0$ for all $i≠c$ is completely encoded in homological properties of $H_I^c(R),$ in particular in its Bass numbers.