On an Instance of the Small Cohen-Macaulay Conjecture

Abstract

We provide a simplified proof of a theorem proved by Tavanfar and Shimomoto which states that a quasi-Gorenstein deformation of a $3$-dimensional quasi-Gorenstein local ring $(A,m,k)$ with $H_m^2(A)=k$ admits a small Cohen-Macaulay module.

arXiv comment5 pages; Expanded Introduction; To appear in J. Pure Appl. Algebra