Thick subcategories over Gorenstein local rings that are locally hypersurfaces on the punctured spectra

TL;DR

This paper classifies thick subcategories in derived and module categories over Gorenstein local rings that are locally hypersurfaces on the punctured spectrum, revealing structural relationships among these categories.

Contribution

It provides a comprehensive classification of thick subcategories over a specific class of Gorenstein rings, connecting derived, module, and Cohen-Macaulay categories.

Findings

Classification of thick subcategories in the bounded derived category.

Classification of thick subcategories of finitely generated modules.

Relationships between subcategories of Cohen-Macaulay modules.

Abstract

Let R be a Gorenstein local ring which is locally a hypersurface on the punctured spectrum. In this paper, we classify thick subcategories of the bounded derived category of finitely generated R-modules. Moreover, using this classification, we also classify thick subcategories of finitely generated R-modules, and find out the relationships with thick subcategories of Cohen-Macaulay R-modules.