Homology, Homotopy and Applications

Volume 22 (2020)

Number 2

The non-nil-invariance of periodic topological cyclic homology

Pages: 173 – 179

DOI: https://dx.doi.org/10.4310/HHA.2020.v22.n2.a11


Ryo Horiuchi (National Institute of Technology (KOSEN), Kure College, Kure, Hiroshima, Japan)


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.


topological periodic cyclic homology, nil-invariance

2010 Mathematics Subject Classification

13D03, 19D55, 55P43

Copyright © 2020, Ryo Horiuchi. Permission to copy for private use granted.

Received 30 January 2019

Received revised 4 July 2019

Accepted 13 September 2019

Published 15 April 2020