H.-B. Foxby and S. Iyengar,
Depth and amplitude for unbounded complexes

Abstract.
We prove that over a commutative noetherian ring the three
approaches to introducing depth for complexes: via Koszul
homology, via Ext module, and via local cohomology, all
yield the same invariant. Using this result, we establish
a far reaching generalization of the classical Auslander-
Buchsbaum formula for the depth of finitely generated
modules of finite projective dimension. We extend also
Iversen's amplitude inequality to unbounded complexes. As
a corollary we deduce: Given a local homomorphism $Q 
\rightarrow R$, if there is a non-zero finitely generated
$R$-module that has finite flat dimension both over $Q$
and over $R$, then the flat dimension of $R$ over $Q$ is
finite. This last result yields a module theoretic
extension of a characterization of regular local rings in
characteristic $p$ due to Kunz and Rodicio