Lemma 29.43.3. An H-projective morphism is H-quasi-projective. An H-projective morphism is projective.

**Proof.**
The first statement is immediate from the definitions. The second holds as $\mathbf{P}^ n_ S$ is a projective bundle over $S$, see Constructions, Lemma 27.21.5.
$\square$

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