Lemma 38.16.7. Let $i : Z \to X$ be a closed immersion of schemes of finite type over a scheme $S$. Let $s \in S$. Let $\mathcal{F}$ be a finite type, quasi-coherent sheaf on $Z$. Then $\mathcal{F}$ is (universally) pure along $Z_ s$ if and only if $i_*\mathcal{F}$ is (universally) pure along $X_ s$.

**Proof.**
This follows from Divisors, Lemma 31.8.3.
$\square$

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