## Algebraic & Geometric Topology

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

Morten Brun

#### 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 $Ki(ℤ∕pn)$ for $i≤p−3$.

#### Article information

Source
Algebr. Geom. Topol., Volume 1, Number 1 (2001), 201-230.

Dates
Revised: 16 March 2001
Accepted: 13 April 2001
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882590

Digital Object Identifier
doi:10.2140/agt.2001.1.201

Mathematical Reviews number (MathSciNet)
MR1823499

Zentralblatt MATH identifier
0984.19001

#### Citation

Brun, Morten. Filtered topological cyclic homology and relative K–theory of nilpotent ideals. Algebr. Geom. Topol. 1 (2001), no. 1, 201--230. doi:10.2140/agt.2001.1.201. https://projecteuclid.org/euclid.agt/1513882590

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