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Towards topological Hochschild homology of Johnson–Wilson spectra

Christian Ausoni and Birgit Richter

Algebraic & Geometric Topology 20 (2020) 375–393

We present computations in Hochschild homology that lead to results on the K(i)–local behaviour of THH(E(n)) for all n 2 and 0 i 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 E3–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–structure. If E(2) is admits an E3–structure, we obtain a similar splitting of the cofiber of the unit map E(2) THH(E(2)).

topological Hochschild homology, Johnson–Wilson spectra, $E_\infty$–structures on ring spectra, chromatic squares
Mathematical Subject Classification 2010
Primary: 55N35, 55P43
Received: 4 October 2018
Revised: 29 March 2019
Accepted: 12 June 2019
Published: 23 February 2020
Christian Ausoni
LAGA (UMR7539)
Institut Galilée
Université Paris 13
Birgit Richter
Fachbereich Mathematik
Universität Hamburg