Lemma 70.11.9. In Situation 70.11.1. If $\mathcal{O}_ X \to \mathcal{A}_0$ is an integral algebra map^{1} and $\mathcal{A}$ is of finite type as an $\mathcal{A}_0$-algebra, then $\pi : \underline{\text{Proj}}_ X(\mathcal{A}) \to X$ is universally closed.

**Proof.**
By Morphisms of Spaces, Lemma 66.9.5 and the construction of the relative Proj this follows from the case of schemes which is Divisors, Lemma 31.30.3.
$\square$

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