\(K\)-theory theorems in topological cyclic homology
type: Item
instance of: scholarly article
title: \(K\)-theory theorems in topological cyclic homology
zbMATH Open document ID: 0932.19003
DOI: 10.1016/S0022-4049(97)00083-2
author: Bjørn Ian Dundas
published in: Journal of Pure and Applied Algebra
publication date: 1999-08-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 19D55
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 18D99
zbMATH DE Number: 1308186
zbMATH Keywords: topological cyclic homology
zbMATH Keywords: topological Hochschild homology
zbMATH Keywords: devissage
zbMATH Keywords: localization
zbMATH Keywords: homotopy invariance
reviewed by: Frédéric Patras
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1308186