Lemma 37.58.3. A flat base change of a pseudo-coherent morphism is pseudo-coherent.

**Proof.**
This translates into the following algebra result: Let $A \to B$ be a pseudo-coherent ring map. Let $A \to A'$ be flat. Then $A' \to B \otimes _ A A'$ is pseudo-coherent. This follows from the more general More on Algebra, Lemma 15.81.12.
$\square$

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