On the category of cofinite complexes and modules

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$. In this paper, we extend Hartshorne's characterization of cofinite complexes to more general classes of rings. We also determine conditions under which Hartshorne's fourth question [H1] admits an affirmative answer. Finally, we investigate the cofiniteness of complexes of $\frak a$-cofinite modules for rings of lower dimensions.