Thick subcategories in stable homotopy theory

Abstract

In these lectures we give an exposition of the seminal work of Devinatz, Hopkins and Smith which is surrounding the classification of the thick subcategories of finite spectra in stable homotopy theory. The lectures are expository and are aimed primarily at non-homotopy theorists. We begin with an introduction to the stable homotopy category of spectra, and then talk about the celebrated thick subcategory theorem and discuss a few applications to the structure of the Bousfield lattice. Most of the results that we discuss here were conjectured by Ravenel \cite{rav} and were proved by Devinatz, Hopkins, and Smith in \cite{dhs, hs}.