Definition 29.37.1. Let $f : X \to S$ be a morphism of schemes. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. We say $\mathcal{L}$ is *relatively ample*, or *$f$-relatively ample*, or *ample on $X/S$*, or *$f$-ample* if $f : X \to S$ is quasi-compact, and if for every affine open $V \subset S$ the restriction of $\mathcal{L}$ to the open subscheme $f^{-1}(V)$ of $X$ is ample.

[II Definition 4.6.1, EGA]

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