Lemma 109.39.1. There exists a morphism of affine schemes of finite presentation $X \to S$ and an $\mathcal{O}_ X$-module $\mathcal{F}$ of finite presentation such that $\mathcal{F}$ is pure relative to $S$, but not universally pure relative to $S$.

**Proof.**
See discussion above.
$\square$

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