Lemma 88.20.5 (0GD1)—The Stacks project

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Part 5: Topics in Geometry
Chapter 88: Algebraization of Formal Spaces
Section 88.20: Rig-étale morphisms
Lemma 88.20.5 (cite)

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Lemma 88.20.5. 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 87.21.10 and the discussion in Formal Spaces, Section 87.23, this follows from Lemma 88.19.4. $\square$

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