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What is the "base change property" of topological Hochschild homology?

In Proposition 11.10 of Bhatt-Morrow-Scholze's paper "Topological Hochschild homology and integral p-adic Hodge theory", they use the base change property of topological Hochschild homolog to calculate $\text{THH}(\mathcal{O}_K/S[z];\mathbb{Z}_p)$ and the calculation of topological Hochschild homology of perfectoid rings, where $K$ is a discretely valued extension of $\mathbb{Q}_p$ and $\mathcal{O}_K$ is the ring of integers.

My understanding is that the base change property of topological Hochschild homology refers to the following claim: for a $\mathbb{E}_\infty$-algebra $R$ and a $\mathbb{E}_\infty$-$R$-algebra $R'$, $\text{THH}(R'/R)$ is defined by $$ \text{THH}(R')\otimes_{\text{THH}(R)}R. $$

However, this property does not work to calculate $\text{THH}(\mathcal{O}_K/S[z];\mathbb{Z}_p)$ since $\text{THH}(\mathcal{O}_K;\mathbb{Z}_p)$ is not calculated in the paper.

What is the "base change property" of topological Hochschild homology which Bhatt-Morrow-Scholze use? and how to calculate $\text{THH}(\mathcal{O}_K/S[z];\mathbb{Z}_p)$?

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    $\begingroup$ Base change should be Cor 11.8, namely along the faithfully flat map $\mathbb S[z]\to\mathbb S[z^{1/p^\infty}]$, I think. $\endgroup$
    – Z. M
    Commented Jan 1, 2023 at 20:57
  • $\begingroup$ @Z.M. It is perfect! Thanks to you I finally understand. the proof of Prop 11.10. Thank you very much! $\endgroup$
    – K.M.
    Commented Jan 1, 2023 at 22:50

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