Algebraic and Geometric Topology 1 (2001), paper no. 10, pages 201-230.

Filtered Topological Cyclic Homology and relative K-theory of nilpotent ideals

Morten Brun

Abstract. In this paper we examine certain filtrations of topological Hochschild homology and topological cyclic homology. 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 K_i(Z/p^m) for i < p-2.

Keywords. K-theory, topological Hochschild homology, cyclic homology, topological cyclic homology

AMS subject classification. Primary: 19D55. Secondary: 19D50, 55P42.

DOI: 10.2140/agt.2001.1.201

E-print: arXiv:math.AT/0104240

Submitted: 17 October 2000. (Revised: 16 March 2001.) Accepted: 13 April 2001. Published: 14 April 2001.

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Morten Brun
Institut de Recherche Mathematique Avancee
CNRS et Universite Louis Pasteur, 7 rue R. Descartes
67084 Strasbourg Cedex, France

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