The Stacks project

Lemma 87.20.5. Let $S$ be a scheme. Let $f : X \to Y$ and $g : Z \to Y$ be morphisms of locally Noetherian formal algebraic spaces over $S$. If $f$ is rig-étale and $g$ is adic, then the base change $X \times _ Y Z \to Z$ is rig-étale.

Proof. By Formal Spaces, Remark 86.21.10 and the discussion in Formal Spaces, Section 86.23, this follows from Lemma 87.19.4. $\square$


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