The non-nil-invariance of periodic topological cyclic homology

Periodic topological cyclic homology $\operatorname{TP}$ is a topological analogue of periodic cyclic homology $\operatorname{HP}$. It is known that, for R an algebra over a field of characteristic $0$ and $I$ a nilpotent ideal of $R$, the quotient map $R \to R/I$ induces an isomorphism on $\operatorname{HP}$. In this paper, we show that the analogous result for $\operatorname{TP}$ does not hold.

Keywords

topological periodic cyclic homology, nil-invariance

2010 Mathematics Subject Classification

13D03, 19D55, 55P43

Full Text (PDF format)

Received 30 January 2019

Received revised 4 July 2019

Accepted 13 September 2019

Published 15 April 2020