[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. $\square$

Comment #2703 by Matt Stevenson on

This is EGA II Cor 4.6.6

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).