Towards topological Hochschild homology of Johnson–Wilson spectra

Ausoni, Christian; Richter, Birgit

doi:10.2140/agt.2020.20.375

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Towards topological Hochschild homology of Johnson–Wilson spectra

Christian Ausoni and Birgit Richter

Algebraic & Geometric Topology 20 (2020) 375–393

DOI: 10.2140/agt.2020.20.375

Abstract

We present computations in Hochschild homology that lead to results on the $K (i)$ –local behaviour of $THH (E (n))$ for all $n \geq 2$ and $0 \leq i \leq n$ , where $E (n)$ is the Johnson–Wilson spectrum at an odd prime. This permits a computation of $K {(i)}_{*} THH (E (n))$ under the assumption that $E (n)$ is an $E_{3}$ –ring spectrum. We offer a complete description of $THH (E (2))$ as an $E (2)$ –module in the form of a splitting into chromatic localizations of $E (2)$ , under the assumption that $E (2)$ carries an $E_{\infty}$ –structure. If $E (2)$ is admits an $E_{3}$ –structure, we obtain a similar splitting of the cofiber of the unit map $E (2) \to THH (E (2))$ .

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Keywords

topological Hochschild homology, Johnson–Wilson spectra, $E_\infty$–structures on ring spectra, chromatic squares

Mathematical Subject Classification 2010

Primary: 55N35, 55P43

References

Publication

Received: 4 October 2018

Revised: 29 March 2019

Accepted: 12 June 2019

Published: 23 February 2020

Authors

Christian Ausoni
LAGA (UMR7539) Institut Galilée Université Paris 13 Villetaneuse France
http://www.math.univ-paris13.fr/~ausoni/
Birgit Richter
Fachbereich Mathematik Universität Hamburg Hamburg Germany
http://www.math.uni-hamburg.de/home/richter/

Volume 20, issue 1 (2020)