Modules whose minimal free resolutions are self-dual or eventually periodic

TL;DR

This paper investigates conditions under which minimal free resolutions of modules over local rings are self-dual or eventually periodic, linking these properties to syzygy and Ext modules, and revisits known theorems in the area.

Contribution

It characterizes self-duality and periodicity of resolutions using syzygy and Ext modules, extending and recovering existing theorems of Dey.

Findings

Identifies criteria for self-duality of resolutions.

Establishes conditions for eventual periodicity.

Provides new proofs and generalizations of Dey's theorems.

Abstract

Let $R$ be a commutative noetherian local ring. In this paper, we study the self-duality and eventual periodicity of minimal free resolutions of finitely generated $R$-modules in terms of their syzygy modules and Ext modules. As an application, we recover theorems of Dey.