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

Brun, Morten¹

¹Institut de Recherche Mathematique Avancée, CNRS et Université Louis Pasteur, 7 rue R. Descartes, 67084 Strasbourg Cedex, France

Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 201-230

Résumé

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.

Détail

DOI : 10.2140/agt.2001.1.201

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

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