\(K\)-theory theorems in topological cyclic homology
Topological cyclic homology (TC) has been developed in order to approximate algebraic \(K\)-theory. The two theories are related by Bökstedt's cyclotomic trace, see the survey [\textit{I. Madsen}, ``Algebraic \(K\)-theory and traces'', in: R. Bott et al. (eds.), Current developments in mathematics 1995, 191-321 (1994) (preliminary version), 135-189 (1995; Zbl 0876.55004) (preliminary partial version with a different title)] for details. It is a fundamental question to understand the differences between the two theories, in particular which properties of algebraic \(K\)-theory remain true for TC or for topological Hochschild homology. This paper addresses the localization and devissage properties. The main results are versions of devissage and ``vanishing of nil-terms'' theorems for TC and topological Hochschild homology. They provide a deeper insight into the differences between \(K\)-theory and TC with respect to homotopy invariance properties.
scientific article; zbMATH DE number 1308186
scientific article