On the Greenlees-May Duality and the Matlis-Greenlees-May Equivalence

Let A be a commutative unital ring and a an ideal in it. We define and study a-reduced complexes and a-coreduced complexes in both the category of chain complexes of A-modules as well as in the derived category of A-modules. We show that these two types of complexes give rise to variants of the well known Greenlees-May duality and the Matlis-Greenlees-May equivalence in the aforementioned categories.