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Filtered topological cyclic homology and relative K–theory of nilpotent ideals

Morten Brun

Algebraic & Geometric Topology 1 (2001) 201–230

arXiv: math.AT/0104240

Abstract

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 nilpotent ideal gives rise to an analog of a theorem of Goodwillie saying that rationally relative K–theory and relative cyclic homology agree. Our variation says that the p–torsion parts agree in a range of degrees. We use it to compute Ki(pn) for i p 3.

Keywords
$K$–theory, topological Hochschild homology, cyclic homology, topological cyclic homology
Mathematical Subject Classification 2000
Primary: 19D55
Secondary: 19D50, 55P42
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Publication
Received: 17 October 2000
Revised: 16 March 2001
Accepted: 13 April 2001
Published: 14 April 2001
Authors
Morten Brun
Institut de Recherche Mathematique Avancée
CNRS et Université Louis Pasteur
7 rue R. Descartes
67084 Strasbourg Cedex
France