Lemma 31.13.13. Let f : X \to Y be a morphism of schemes. Let D \subset Y be an effective Cartier divisor. The pullback of D by f is defined in each of the following cases:
f(x) \not\in D for any weakly associated point x of X,
X, Y integral and f dominant,
X reduced and f(\xi ) \not\in D for any generic point \xi of any irreducible component of X,
X is locally Noetherian and f(x) \not\in D for any associated point x of X,
X is locally Noetherian, has no embedded points, and f(\xi ) \not\in D for any generic point \xi of an irreducible component of X,
f is flat, and
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