Topological Hochschild homology of truncated Brown–Peterson spectra, I

Angelini-Knoll, Gabriel; Culver, Dominic Leon; Höning, Eva

doi:10.2140/agt.2024.24.2509

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

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

DOI: 10.2140/agt.2024.24.2509

Abstract

We compute the topological Hochschild homology of sufficiently structured forms of truncated Brown–Peterson spectra with coefficients. In particular, we compute ${THH}_{*} (B ⟨ n ⟩; H ℤ_{(p)})$ for all $n$ , where $B ⟨ n ⟩$ is an $E_{3}$ form of $BP ⟨ n ⟩$ for certain primes $p$ , and ${THH}_{*} (B ⟨ 2 ⟩; M)$ for $M \in {k (1), k (2)}$ . For example, this gives a computation of $THH ({taf}^{D}; M)$ for $M \in {H ℤ_{(3)}, k (1), k (2)}$ where ${taf}^{D}$ is the $E_{\infty}$ 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

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 5 (2024)