The author introduces the notion of a Galois extension of commutative $ S $-algebras ($
E_\infty $ ring spectra), often localized with respect to a fixed homology theory. There are …

Introduction 1 1. Spectra and the stable homotopy category 6 2. Smash products and twisted
half-smash products 11 3. The category of L-spectra 13 4. The smash product of L-spectra …

To a “stable homotopy theory”(a presentable, symmetric monoidal stable∞-category), we
naturally associate a category of finite étale algebra objects and, using Grothendieck's …

We define an inner product (suitably interpreted) on the K (n)-local spectrum LG:= L_ {K (n)}
BG_+, where G is a finite group or groupoid. This gives an inner product on E^* BG_+ for …

In this paper we advertise the category of Γ-spaces as a convenient framework for doing
'algebra'over 'rings' in stable homotopy theory. Γ-spaces were introduced by Segal [Se] who …

Let E be a homotopy commutative ring spectrum, and suppose the ring of cooperations E∗ E
is flat over E∗. We wish to address the following question: given a commutative E∗-algebra …

In this document we make good on all the assertions we made in the previous paper “Moduli
spaces of commutative ring spectra”[20] wherein we laid out a theory a moduli spaces and …

We prove that the stable homotopy of any Γ-module F is the homology of a bicomplex Ξ (F),
in which the (q− 1) st row is the two-sided bar construction ℬ (Lie* q, Σ q, F [q]). This gives a …

To a topological group G, we assign a naive G-spectrum D_G, called the dualizing spectrum
of G. When the classifying space BG is finitely dominated, we show that D_G detects …

This book introduces a new point-set level approach to stable homotopy theory that has
already had many applications and promises to have a lasting impact on the subject. Given …