Lemma 27.5.8. Any morphism of schemes $f : X \to Y$ with $X$ Noetherian is quasi-compact.

**Proof.**
Use Lemma 27.5.5 and use that any subset of a Noetherian topological space is quasi-compact (see Topology, Lemmas 5.9.2 and 5.12.13).
$\square$

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