Nilpotence and Descent in Stable Homotopy Theory

Abstract

We study various applications of the ideas of descent and nilpotence to stable homotopy theory. In particular, we give a descent-theoretic calculation of the Picard group of topological modular forms and we prove a partial analog of Thomason’s etale descent theorem in the algebraic K-theory of ring spectra. In addition, we prove thick subcategory theorems for certain ring spectra and give a new proof of a classical result of Dade on endotrivial modules for abelian p-groups.