The Stacks project

Lemma 76.23.6. Let $S$ be a scheme. Let $f : X \to Y$ and $Y \to Z$ be a morphism of algebraic spaces over $S$. Assume

  1. $X$ is locally of finite presentation over $Z$,

  2. $X$ is flat over $Z$, and

  3. $Y$ is locally of finite type over $Z$.

Then the set

\[ \{ x \in |X| : X\text{ flat at }x \text{ over }Y\} . \]

is open in $|X|$ and its formation commutes with arbitrary base change $Z' \to Z$.

Proof. This is a special case of Lemma 76.23.5. $\square$

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