Constructing Big Indecomposable modules

TL;DR

This paper constructs large indecomposable modules over certain local rings, demonstrating their existence with specific properties related to the ring's depth and module rank.

Contribution

It proves the existence of indecomposable modules that are free on the punctured spectrum with arbitrarily large, constant rank over local Noetherian rings of depth at least two.

Findings

Existence of indecomposable modules with specified properties

Modules are free on punctured spectrum

Modules can have arbitrarily large, constant rank

Abstract

Let $R$ be local Noetherian ring of depth at least two. We prove that there are indecomposable $R$-modules which are free on the punctured spectrum of constant, arbitrarily large, rank.