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

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 $K_{i} (ℤ ∕ p^{n})$ for $i \leq p - 3$ .

Keywords

$K$–theory, topological Hochschild homology, cyclic homology, topological cyclic homology

Mathematical Subject Classification 2000

Primary: 19D55

Secondary: 19D50, 55P42

References

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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

Volume 1, issue 1 (2001)

Morten Brun