- Let A be a commutative noetherian ring, and an ideal in it. In this paper we continue the study, begun in [1111. Porta , M. , Shaul , L. , Yekutieli , A. On the homology of completion and torsion . Algebr. Represent. Theor. (published online 2012 , doi: DOI 10.1007/s10468-012-9385-8) . [Web of Science ®]View all references], of the derived -adic completion and the derived -torsion functors. Here are our results: (1) a structural characterization of bounded above cohomologically complete complexes; (2) the Cohomologically Complete Nakayama Theorem; and (3) a characterization of cohomologically cofinite complexes.