This volume introduces equivariant homotopy, homology, and cohomology theory, along
with various related topics in modern algebraic topology. It explains the main ideas behind …

The purpose of this paper is twofold. Firstly, it gives a thorough introduction to the topological
cyclic homology theory, which to a ring R associates a spectrum TC (R). We determine TC …

Hodge theory, since its appearance in complex analysis, has long become one of the most
useful tools in complex algebraic geometry. At the core of its algebraic applications lies a …

Let f: A-~ B be a map of rings up to homotopy (or" FSP's", see eg [B61],[B53] or Definition 3.1
below). When is it possible to give a good description of the relative algebraic K-theory …

This survey is about homotopy types of spaces of automorphisms of topological and smooth
manifolds. Most ofthe results available are relative, ie, they compare different types of …

Classically, one has for every commutative ring A the associated ring of p-typical Witt vectors
W (A). In this paper we extend the classical construction to a functor which associates to any …

We calculate the A (1)-homotopy of the topological cyclic homology of the connective real
topological K-theory spectrum ko, and show that it is a finitely generated and free F_2 …

We construct a category of spectra that has all limits and colimits and also has a strictly
associative and commutative smash product. This provides the ground category for a new …

1.1. Topological cyclic homology is the codomain of the cyclotomic trace from algebraic i^-
theory trc: K (L)-> TC (L). It was defined in [2] but for our purpose the exposition in [6] is more …

We embed the Lubin-Tate tower into a larger tower of formal schemes, the" degenerating
Lubin-Tate tower." We construct a topological realization of the degenerating Lubin-Tate …