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

TL;DR

This paper explores variants of Greenlees-May duality and the Matlis-Greenlees-May equivalence by defining and analyzing a-reduced and a-coreduced complexes within the derived category of modules over a commutative ring.

Contribution

It introduces and studies a-reduced and a-coreduced complexes, extending Greenlees-May duality and the Matlis-Greenlees-May equivalence to these new contexts.

Findings

Defined a-reduced and a-coreduced complexes in derived categories.

Established variants of Greenlees-May duality using these complexes.

Extended the Matlis-Greenlees-May equivalence to new complex categories.

Abstract

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.