Remark 100.9.19. Warning: Lemma 100.9.18 should be used with care. For example, it applies to $\mathcal{P}=$“flat”, $\mathcal{Q}=$“empty”, and $\mathcal{R}=$“flat and locally of finite presentation”. But given a morphism of algebraic spaces $f : X \to Y$ the largest open subspace $W \subset X$ such that $f|_ W$ is flat is *not* the set of points where $f$ is flat!

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