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Topological Hochschild homology of truncated Brown–Peterson spectra, I

Gabriel Angelini-Knoll, Dominic Leon Culver and Eva Höning

Algebraic & Geometric Topology 24 (2024) 2509–2536
Abstract

We compute the topological Hochschild homology of sufficiently structured forms of truncated Brown–Peterson spectra with coefficients. In particular, we compute THH (Bn;H(p)) for all n, where Bn is an E3 form of BP n for certain primes p, and THH (B2;M) for M {k(1),k(2)}. For example, this gives a computation of THH (taf D;M) for M {H(3),k(1),k(2)} where taf D is the E form of BP 2 constructed by Hill and Lawson.

Keywords
topological Hochschild homology, truncated Brown–Peterson spectra, Bockstein spectral sequences
Mathematical Subject Classification
Primary: 16E40, 19D55, 55N22, 55P43, 55Q51
Secondary: 55P42, 55Q10, 55T99
References
Publication
Received: 24 June 2021
Revised: 4 May 2023
Accepted: 12 July 2023
Published: 19 August 2024
Authors
Gabriel Angelini-Knoll
Universite Sorbonne Paris Nord, LAGA, CNRS
Villetaneuse
France
Dominic Leon Culver
Max Planck Institute for Mathematics
Bonn
Germany
Eva Höning
Department of Mathematics
Radboud University
Nijmegen
Netherlands

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