Equivalences from tilting theory and commutative algebra from the adjoint functor point of view

TL;DR

This paper uses category theory to unify known equivalences in tilting theory and commutative algebra, and applies these results to develop a duality theory for relative Cohen-Macaulay modules.

Contribution

It introduces a category theoretic framework to connect tilting theory and commutative algebra, and extends duality concepts to relative Cohen-Macaulay modules.

Findings

Unified several known equivalences via category theory.

Established a duality theory for relative Cohen-Macaulay modules.

Provided new insights into the structure of tilting and Cohen-Macaulay modules.

Abstract

We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen-Macaulay modules in the sense of Hellus, Schenzel, and Zargar.