Lemma 71.9.1. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S. Let D \subset X be a closed subspace. Assume
D is an effective Cartier divisor, and
D \to Y is a flat morphism.
Then for every morphism of schemes g : Y' \to Y the pullback (g')^{-1}D is an effective Cartier divisor on X' = Y' \times _ Y X where g' : X' \to X is the projection.
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