On Cohen-Macaulay modules over non-commutative surface singularities

TL;DR

This paper extends Kahn's correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities, providing examples that are tame but not finite.

Contribution

It generalizes the Cohen-Macaulay correspondence to non-commutative settings and offers new examples illustrating tame versus finite classification.

Findings

Extended Cohen-Macaulay correspondence to non-commutative surfaces

Identified non-commutative surface singularities that are tame but not finite

Provided explicit examples illustrating the classification distinctions

Abstract

We generalize the results of Kahn about a correspondence between Cohen-Macaulay modules and vector bundles to non-commutative surface singularities. As an application, we give examples of non-commutative surface singularities which are not Cohen-Macaulay finite, but are Cohen-Macaulay tame.