TITLE: Confusion about topological Hochschild homology and $\mathbb{Z}_p$-topological Hochschild homology
QUESTION [6 upvotes]: Let $R$ be the ring of integers in a perfectoid field of mixed characteristic $p$. Is $\pi_*THH(R)$ (as defined in Bhatt--Morrow--Scholze) $p$-complete (as an abelian group)?

REPLY [3 votes]: Remark 6.1. here  seems to imply that the answer is no: "When the input ring $A$ is $p$-adically complete (but not killed
by a power of p), then $HH(A/\mathbb{Z}_p)$, $THH(A)$, etc., as we have already defined them, will contain large
amounts of undesirable, junk data."