In the first part of this thesis the homotopy theory of operads, algebras over operads and
modules over operad algebras is developed in the context of cofibrantly generated …

We prove that if a category has two Quillen closed model structures (W1, F1, C1) and (W2,
F2, C2) that satisfy the inclusions W1⊆ W2 and F1⊆ F2, then there exists a “mixed model …

We construct triangulated categories of mixed motives over a noetherian scheme of finite
dimension, extending Voevodsky's definition of motives over a field. We prove that motives …

We verify a conjecture of Rognes by establishing a localization cofiber sequence of spectra
K(Z)→K(ku)→K(KU)→ΣK(Z) for the algebraic K-theory of topological K-theory. We deduce …

We study the structure possessed by the Goodwillie derivatives of a pointed homotopy
functor of based topological spaces. These derivatives naturally form a bimodule over the …

This chapter explains how the solution of the Ravenel Conjectures by Ethan S. Devinatz,
Michael J. Hopkins, DC Ravenel, and Jeffrey H. Smith leads to a canonical filtration in stable …

The purpose of this paper is to describe a connection between model categories, a structure
invented by algebraic topologists that allows one to introduce the ideas of homotopy theory …

This textbook is an introduction to the modern foundations of stable homotopy theory and
'algebra'over structured ring spectra, based on symmetric spectra. We begin with a quick …

A functor is defined which detects stable equivalences of symmetric spectra. As an
application, the definition of topological Hochschild homology on symmetric ring spectra …

We study the indexing systems that correspond to equivariant Steiner and linear isometries
operads. When G is a finite abelian group, we prove that a G-indexing system is realized by …