#### Volume 1, issue 1 (2001)

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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 ${K}_{i}\left(ℤ∕{p}^{n}\right)$ for $i\le p-3$.

##### Keywords
$K$–theory, topological Hochschild homology, cyclic homology, topological cyclic homology
##### Mathematical Subject Classification 2000
Primary: 19D55
Secondary: 19D50, 55P42