Given a henselian pair $(R, I) $ of commutative rings, we show that the relative $ K $-theory
and relative topological cyclic homology with finite coefficients are identified via the …

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 …

The purpose of this paper is to study pro excision in algebraic K-theory and cyclic homology,
after Suslin–Wodzicki, Cuntz–Quillen, Cortiñas, and Geisser–Hesselholt, as well as …

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 …

Topological cyclic homology is a manifestation of Waldhausen's vision that the cyclic theory
of Connes and Tsygan should be developed with the initial ring S of higher algebra as base …

In recent years, the study of the algebraic K-theory space K (R) of a ring R has been
approached by the introduction of spaces with a more homological flavor. One collection of …

We prove that the Farrell–Jones assembly map for connective algebraic K-theory is
rationally injective, under mild homological finiteness conditions on the group and assuming …

We give a survey of cyclic homology/cohomology theory including a detailed discussion of
cyclic theories for various classes of topological algebras. We show how to associate cyclic …

This paper reviews the relations between algebraic K-theory and topological cyclic
homology given by cyclotomic trace. If one, very superficially, views algebraic K-theory as …

Topological cyclic homology is a refinement of Connes–Tsygan's cyclic homology which
was introduced by Bökstedt–Hsiang–Madsen in 1993 as an approximation to algebraic K …