Let A→ B be a G-Galois extension of rings, or more generally of E∞-ring spectra in the
sense of Rognes. A basic question in algebraic K-theory asks how close the map K (A)→ K …

We give a full classification of representation types of the subcategories of representations of
an m× n rectangular grid with monomorphisms (dually, epimorphisms) in one or both …

This chapter discusses non-technical account of some ideas in the theory of∞-categories,
as originally introduced by Boardman–Vogt in their study of homotopy-invariant algebraic …

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 …

This paper interprets Hesselholt and Madsen's real topological Hochschild homology functor
THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality …

We extend the Chern character on K-theory, in its generalization to the Chern-Dold
character on generalized cohomology theories, further to (twisted, differential) non-abelian …

We show that a well behaved Noetherian, finite dimensional, stable, monoidal model
category has a model built from categories of modules over completed rings in an adelic …

Given an exact symplectic manifold M and a support Lagrangian Λ⊂ M, we construct an∞-
category Lag Λ (M) which we conjecture to be equivalent (after specialization of the …

Goodwillie calculus is a method for analyzing functors that arise in topology. One may think
of this theory as a categorification of the classical differential calculus of Newton and …

We collect in one place a variety of known and folklore results in enriched model category
theory and add a few new twists. The central theme is a general procedure for constructing a …