  We investigate the similarities between adic finiteness and homological
finiteness for chain complexes over a commutative noetherian ring. In
particular, we extend the isomorphism properties of certain natural morphisms
from homologically finite complexes to adically finite complexes. We do the
same for characterizations of certain homological dimensions. In addition, we
study transfer of adic finiteness along ring homomorphisms, all with a view
toward subsequent applications.
