K-theory theorems in topological cyclic homology Original Research Article

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? In addition to confinality, resolution and finite products which have been previously discussed for topological Hochschild homology, this paper addresses localization and Devissage. Its main result is a Devissage theorem and a “vanishing of nil-terms” result for topological Hochschild homology and topological cyclic homology.