The Greenless-May Duality and the MGM Equivalence in the category of chain complexes

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. ; Comment: 14 pages