Lemma 77.3.5. In Situation 77.2.1. Let $i : Z \to X$ be a closed immersion and assume that $\mathcal{F} = i_*\mathcal{G}$ for some finite type, quasi-coherent sheaf $\mathcal{G}$ on $Z$. Then $\mathcal{G}$ is (universally) pure above $y$ if and only if $\mathcal{F}$ is (universally) pure above $y$.

**Proof.**
This follows from Divisors on Spaces, Lemma 71.4.9.
$\square$

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