Algebraic & Geometric Topology

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

Morten Brun

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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(pn) for ip3.

Article information

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

Received: 17 October 2000
Revised: 16 March 2001
Accepted: 13 April 2001
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology [See also 18G60]
Secondary: 19D50: Computations of higher $K$-theory of rings [See also 13D15, 16E20] 55P42: Stable homotopy theory, spectra

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


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.

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