Definition 70.14.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. We say $\mathcal{L}$ is relatively ample, or $f$-relatively ample, or ample on $X/Y$, or $f$-ample if $f : X \to Y$ is representable and for every morphism $Z \to Y$ where $Z$ is a scheme, the pullback $\mathcal{L}_ Z$ of $\mathcal{L}$ to $X_ Z = Z \times _ Y X$ is ample on $X_ Z/Z$ as in Morphisms, Definition 29.37.1.

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