Lemma 71.11.9. In Situation 71.11.1. If \mathcal{O}_ X \to \mathcal{A}_0 is an integral algebra map1 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 67.9.5 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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