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 serves as an approximation to algebraic K-theory. It is more
accessible to calculations, but how well does it reflect the structural properties of K-theory …

Abstract The Topological Hochschild Homology (THH) of a ring R, and, more generally, of a"
strictly associative" ring spectrum F, is a spectrum with an action of the circle. The topological …

In this paper certain filtrations of topological Hochschild homology and topological cyclic
homology are examined. As an example we show how the filtration with respect to a …

The topological Hochschild homology of the integers T (Z)= THH (Z) is an S1-equivariant
spectrum. We prove by computation that for the restricted C2-action on T (Z) the fixed points …

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 …

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 …

If A is a homotopy cartesian square of ring spectra satisfying connectivity hypotheses, then
the cube induced by Goodwillie's integral cyclotomic trace K(A)→TC(A) is homotopy …

In this note we use a topological version of Hochschild homology and cyclic homology of a
commutative algebra, introduced by P. Seibt in [Se 2], to show, that periodic homology can …

The cyclotomic trace provides a comparison of the algebraic K-theory spectrum and a pro-
spectrum TR that is built from the cyclic fixed points of topological Hochschild homology. In a …