The Stacks project

[II Corollary 4.6.6, EGA]

Lemma 29.37.5. Let $f : X \to S$ be a morphism of schemes. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. Assume $S$ affine. Then $\mathcal{L}$ is $f$-relatively ample if and only if $\mathcal{L}$ is ample on $X$.

Proof. Immediate from Lemma 29.37.4 and the definitions. $\square$


Comments (2)

Comment #2703 by Matt Stevenson on

This is EGA II Cor 4.6.6


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