Lemma 71.14.3. 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. Let Y' \to Y be a morphism of algebraic spaces over S. Let f' : X' \to Y' be the base change of f and denote \mathcal{L}' the pullback of \mathcal{L} to X'. If \mathcal{L} is f-ample, then \mathcal{L}' is f'-ample.
Proof. This follows immediately from the definition! (Hint: transitivity of base change.) \square
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