The Stacks project

Lemma 66.30.11. Let $S$ be a scheme. Let $f : X \to Y$ be a flat morphism of algebraic spaces over $S$. Let $V \to Y$ be a quasi-compact open immersion. If $V$ is scheme theoretically dense in $Y$, then $f^{-1}V$ is scheme theoretically dense in $X$.

Proof. Using the characterization of scheme theoretically dense opens in Lemma 66.17.2 and using the characterization of flat morphisms in terms of ├ętale coverings in Lemma 66.30.5 we reduce to the case of schemes which is Morphisms, Lemma 29.25.15. $\square$


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