On the vanishing of self extensions of even-periodic modules

TL;DR

This paper investigates the properties of rigid modules over commutative Noetherian local rings, providing new criteria for freeness, Ext vanishing results, and insights into modules with trivial classes in the Grothendieck group.

Contribution

It introduces new freeness criteria for periodic rigid modules and extends Ext vanishing results to Cohen-Macaulay rings.

Findings

Established new criteria for freeness of periodic rigid modules

Proved general Ext vanishing results over Cohen-Macaulay rings

Analyzed modules with zero class in the reduced Grothendieck group

Abstract

In this paper we study rigid modules over commutative Noetherian local rings, establish new freeness criteria for certain periodic rigid modules, and extend several results from the literature. Along the way, we prove general Ext vanishing results over Cohen-Macaulay rings and investigate modules which have zero class in the reduced Grothendieck group with rational coefficients.