A Note on The Global Dimension of Shifted Orders

TL;DR

This paper investigates the global dimension of endomorphism rings of certain tilting modules over orders in Cohen-Macaulay rings, providing bounds based on dominant dimension.

Contribution

It introduces an upper bound on the global dimension of endomorphism rings associated with shifted orders in Cohen-Macaulay settings.

Findings

Established an upper bound for the global dimension of endomorphism rings.

Connected dominant dimension with the properties of tilting modules.

Enhanced understanding of the structure of orders over Cohen-Macaulay rings.

Abstract

We consider dominant dimension of an order over a Cohen-Macaulay ring in the category of centrally Cohen-Macaulay modules. There is a canonical tilting module in the case of positive dominant dimension and we give an upper bound on the global dimension of its endomorphism ring.