Refining Thick Subcategory Theorems

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 complexes over some noetherian rings. In the homotopy category of spectra we obtain only a partial classi cation of the triangulated subcategories of the nite p-local spectra. We use this partial classi cation to study the lattice of triangulated subcategories. This study gives some new evidence to a conjecture of Adams that the thick subcategory C2 can be generated by iterated co berings of the Smith-Toda complex We also discuss various consequences of these classi cations theorems.