Topological Hochschild homology of truncated Brown-Peterson spectra I

Abstract

We compute topological Hochschild homology of sufficiently structured forms of truncated Brown--Peterson spectra with coefficients. In particular, we compute ${\mathrm{THH}}_{\ast }(B⟨n⟩;H{\mathbb{Z}}_{(p)})$ for all $n$ and ${\mathrm{THH}}_{\ast }(B⟨2⟩;M)$ for $M\in \{k(1),k(2)\}$ where $B⟨n⟩$ is an $E_3$ form of $BP⟨n⟩$ for certain primes $p$. For example, this gives a computation of $\mathrm{THH}({\mathrm{taf}}^D;M)$ for $M\in \{H{\mathbb{Z}}_{(3)},k(1),k(1))$ where ${\mathrm{taf}}^D$ is the $E_{\infty }$ form of $BP⟨2⟩$ constructed by Hill--Lawson.

27 pages including references. Accepted version. To appear in Algebraic & Geometric Topology

Cited by in corpus (2)

• Algebraic K-theory of elliptic cohomology
• Lifting to truncated Brown-Peterson spectra and Hodge-de Rham degeneration in characteristic $p>0$