Lemma 71.11.7. In Situation 71.11.1. If one of the following holds
\mathcal{A} is of finite type as a sheaf of \mathcal{A}_0-algebras,
\mathcal{A} is generated by \mathcal{A}_1 as an \mathcal{A}_0-algebra and \mathcal{A}_1 is a finite type \mathcal{A}_0-module,
there exists a finite type quasi-coherent \mathcal{A}_0-submodule \mathcal{F} \subset \mathcal{A}_{+} such that \mathcal{A}_{+}/\mathcal{F}\mathcal{A} is a locally nilpotent sheaf of ideals of \mathcal{A}/\mathcal{F}\mathcal{A},
then \pi : \underline{\text{Proj}}_ X(\mathcal{A}) \to X is quasi-compact.
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