  Let $A$ be a commutative unital ring. We prove the MGM equivalence and the
Greenless-May duality in the category of chain complexes of $A$-modules. This
extends the above notions from the category of $A$-modules studied in
\cite{David-Application-I} to the category of chain complexes. Furthermore, it
utilizes a more general setting of reduced and coreduced complexes instead of
the weak proregularity of ideals of $A$ that has hitherto been used to obtain
similar results in the derived category setting.

Rings and Algebras;Commutative Algebra;Representation Theory