Filtered Topological Cyclic Homology and relative K-theory of nilpotent ideals

Details Filtered Topological Cyclic Homology and relative K-theory of nilpotent ideals Filtered Topological Cyclic Homology and relative K-theory of nilpotent ideals

2001-04-25

arxiv.org/abs/math/0104240v1

Algebr. Geom. Topol. 1 (2001) 201-230

Mathematics

Algebraic Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-10.abs.html

Scientific paper

In this paper we examine certain filtrations of topological Hochschild homology and topological cyclic homology. 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^m) for i < p-2.

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