Lemma 29.21.6. Any open immersion is of finite presentation if and only if it is quasi-compact.

Proof. We have seen (Lemma 29.21.5) that an open immersion is locally of finite presentation. We have seen (Schemes, Lemma 26.23.8) that an immersion is separated and hence quasi-separated. From this and Definition 29.21.1 the lemma follows. $\square$

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