The spectrum of a category of maximal Cohen-Macaulay modules

TL;DR

This paper develops a topological framework for maximal Cohen-Macaulay modules over complete Cohen-Macaulay local rings, analyzing their structure and calculating the Cantor-Bendixson rank in specific cases.

Contribution

It introduces an analog of the Ziegler spectrum for maximal Cohen-Macaulay modules and studies its topological properties, including the Cantor-Bendixson rank for rings of finite representation type.

Findings

Defined a topology on the space of indecomposable maximal Cohen-Macaulay modules

Calculated the Cantor-Bendixson rank for CM_+-finite rings

Analyzed the topological structure of the spectrum

Abstract

We introduce an analog of the Ziegler spectrum for maximal Cohen-Macaulay modules over a complete Cohen-Macaulay local ring. We define a topology on the space of isomorphism classes of indecomposable maximal Cohen-Macaulay modules and investigate the topological structure. We also calculate the Cantor-Bendixson rank for a ring which is of CM_+-finite representation type.