We use a K-theory recipe of Thomason to obtain classi cations of triangulated subcategories via re ning some standard thick subcategory theorems. We apply this recipe to the full subcategories of nite objects in the derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classi cation of the triangulated subcategories of perfect...

Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p-group due to Benson, Carlson and Rickard, we consider classifying thick subcategories of th...

In this paper we study wide subcategories. A full subcategory of R-modules is said to be wide if it is abelian and closed under extensions. Hovey [Hov01] gave a classification of wide subcategories of finitely presented modules over regular coherent rings in terms of certain specialisation closed subsets of Spec(R). We use this classification theorem to study K-theory and “Krull-Schmidt” decomp...