#### 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.

Notes on file formats
Morten Brun

Institut de Recherche Mathematique Avancee

CNRS et Universite Louis Pasteur, 7 rue R. Descartes

67084 Strasbourg Cedex, France

Email: brun@math.u-strasbg.fr

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