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

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.