Examples of non-commutative crepant resolutions of Cohen Macaulay normal domains

TL;DR

This paper provides numerous examples of Cohen-Macaulay normal domains, both local and affine, that admit non-commutative crepant resolutions, expanding the known classes of such algebraic structures.

Contribution

The paper introduces a wide variety of examples of Cohen-Macaulay normal domains with non-commutative crepant resolutions in different characteristics and settings.

Findings

Examples of NCCR in equi-characteristic Cohen-Macaulay local domains

Examples of NCCR in mixed characteristic Cohen-Macaulay local domains

Examples of NCCR in affine Cohen-Macaulay normal domains

Abstract

Let $A$ be a Cohen-Macaulay normal domain. A non commutative crepant resolution (NCCR) of $A$ is an $A$-algebra $\Gamma$ of the form $\Gamma = End_A(M)$, where $M$ is a reflexive $A$-module, $\Gamma$ is maximal Cohen-Macaulay as an $A$-module and $gldim(\Gamma)_P = \dim A_P $ for all primes $P$ of $A$. We give bountiful examples of equi-characteristic Cohen-Macaulay normal local domains and mixed characteristic Cohen-Macaulay normal local domains having NCCR. We also give plentiful examples of affine Cohen-Macaulay normal domains having NCCR.