Classifying resolving subcategories over a Cohen-Macaulay local ring

TL;DR

This paper classifies resolving subcategories of finitely generated modules over Cohen-Macaulay local rings, especially those closed under tensor products and transposes, providing new insights into their structure and classification.

Contribution

It offers a classification of resolving subcategories in terms of specialization-closed subsets of the spectrum, with improved results under certain hypotheses.

Findings

Resolved classification of resolving subcategories closed under tensor and transpose operations

Established correspondence between subcategories and specialization-closed subsets of Spec R

Provided refined classification results under restrictive conditions

Abstract

Let R be a Cohen-Macaulay local ring. Denote by mod R the category of finitely generated R-modules. In this paper, we consider the classification problem of resolving subcategories of mod R in terms of specialization-closed subsets of Spec R. We give a classification of the resolving subcategories closed under tensor products and transposes. Under restrictive hypotheses, we also give better classification results.