Linkage of finite G_C-dimension modules

TL;DR

This paper explores the linkage theory of modules with finite G_C-dimension over semiperfect Noetherian rings, connecting Serre conditions with cohomology vanishing in this context.

Contribution

It introduces a linkage framework for modules of finite G_C-dimension and relates Serre conditions to cohomology vanishing for linked modules.

Findings

Linkage theory for finite G_C-dimension modules is developed.

Serre condition (S_n) is connected to cohomology vanishing.

Results apply to horizontally linked modules over semiperfect rings.

Abstract

Let R be a semiperfect commutative Noetherian ring and C a semidualizing R-module. We study the theory of linkage for modules of finite G_C-dimension. For a horizontally linked R-module M of finite G_C-dimension, the connection of the Serre condition (S_n) with the vanishing of certain relative cohomology modules of its linked module is discussed.