Towards topological Hochschild homology of Johnson-Wilson spectra

Abstract

We offer a complete description of $THH(E(2))$ under the assumption that the Johnson-Wilson spectrum $E(2)$ at a chosen odd prime carries an $E_{\infty }$-structure. We also place $THH(E(2))$ in a cofiber sequence $E(2)\to THH(E(2))\to \overline{THH}(E(2))$ and describe $\overline{THH}(E(2))$ under the assumption that $E(2)$ is an $E_3$-ring spectrum. We state general results about the $K(i)$-local behaviour of $THH(E(n))$ for all $n$ and $0\le i\le n$. In particular, we compute $K(i{)}_{\ast }THH(E(n))$.

Submitted version