Topological Hochschild homology of truncated Brown–Peterson spectra, I

Angelini-Knoll, Gabriel¹ ; Culver, Dominic Leon² ; Höning, Eva³

¹ Universite Sorbonne Paris Nord, LAGA, CNRS, Villetaneuse, France
² Max Planck Institute for Mathematics, Bonn, Germany
³ Department of Mathematics, Radboud University, Nijmegen, Netherlands

Algebraic and Geometric Topology, Tome 24 (2024) no. 5, pp. 2509-2536

Résumé

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

Détail

DOI : 10.2140/agt.2024.24.2509

Keywords: topological Hochschild homology, truncated Brown–Peterson spectra, Bockstein spectral sequences