An Alexandrov Topology for Maximal Cohen-Macaulay Modules

TL;DR

This paper introduces a new topology on maximal Cohen-Macaulay modules over Gorenstein rings using cohomology annihilators, and investigates its compactness properties.

Contribution

It defines a novel topology on Cohen-Macaulay modules based on cohomology annihilators and analyzes its topological properties.

Findings

The topology is well-defined on the set of modules.

Certain conditions ensure the compactness of this topology.

The topology provides new insights into the structure of Cohen-Macaulay modules.

Abstract

Using the theory of cohomology annihilators, we define a family of topologies on the set of isomorphism classes of maximal Cohen-Macaulay modules over a Gorenstein ring. We study compactness of these topologies.