Lemma 70.11.6. In Situation 70.11.1 the morphism $\pi : \underline{\text{Proj}}_ X(\mathcal{A}) \to X$ is separated.

**Proof.**
By Morphisms of Spaces, Lemma 66.4.12 and the construction of the relative Proj this follows from the case of schemes which is Constructions, Lemma 27.16.9.
$\square$

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