Title: Refining thick subcategory theorems
Author: Sunil Chebolu
Email address: schebolu@uwo.ca
AMS classifictaion numbers: Primary: 55P42, 18G55, 19A99
Address: Department of Mathematics, University of Western Ontario, London, ON, N6A 5B7
Abstract: 
We use a $K$-theory recipe of Thomason to obtain classifications of triangulated subcategories via
refining some standard thick subcategory theorems. We apply this recipe to the full subcategories of finite objects in the  
derived categories of rings and the stable homotopy category of spectra. This gives, in the derived categories, a complete classification
of the triangulated subcategories of perfect complexes over some noetherian rings. In the homotopy category of spectra we obtain only a partial classification of
the triangulated subcategories of the finite $p$-local spectra. We use this partial classification to study the lattice of triangulated subcategories.
This study gives some  new evidence to a conjecture of Adams that the thick subcategory $\C_2$ can be generated by iterated cofiberings of the Smith-Toda complex
We also discuss various consequences of these classifications theorems.