Linkage of modules over Cohen-Macaulay rings

TL;DR

This paper introduces a new linkage theory for modules over Cohen-Macaulay rings, establishing conditions under which linked modules are Cohen-Macaulay and relating these to existing module-theoretic properties.

Contribution

It defines the sliding depth of extension modules and uses it to prove Cohen-Macaulayness of linked modules, improving and recovering classical linkage results.

Findings

Linked modules are Cohen-Macaulay under new sliding depth conditions

Relations between sliding depth, G-dimension, and sequentially Cohen-Macaulay are established

Several classical linkage theorems are improved or recovered

Abstract

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new condition and other module-theory conditions such as G-dimension and sequentially Cohen-Macaulay are established. By the way several already known theorems in linkage theory are improved or recovered by new approaches.