Lemma 35.20.5. The property $\mathcal{P}(f) =$“$f$ is universally submersive” is fpqc local on the base.

Proof. The proof is the same as the proof of Lemma 35.20.3 using that a quasi-compact flat surjective morphism is universally submersive by Morphisms, Lemma 29.25.12. $\square$

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