Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 1, Number 1 (2001), 201-230.
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 –theory and relative cyclic homology agree. Our variation says that the –torsion parts agree in a range of degrees. We use it to compute for .
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
Permanent link to this document
Digital Object Identifier
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
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