Lemma 29.37.2 (02NN)—The Stacks project

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Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.37: Relatively ample sheaves
Lemma 29.37.2 (cite)

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Lemma 29.37.2. Let $X \to S$ be a morphism of schemes. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. Let $n \geq 1$. Then $\mathcal{L}$ is $f$-ample if and only if $\mathcal{L}^{\otimes n}$ is $f$-ample.

Proof. This follows from Properties, Lemma 28.26.2. $\square$

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