The Stacks project

Lemma 71.6.11. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $D \subset Y$ be an effective Cartier divisor. The pullback of $D$ by $f$ is defined in each of the following cases:

  1. $f(x) \not\in |D|$ for any weakly associated point $x$ of $X$,

  2. $f$ is flat, and

  3. add more here as needed.

Proof. Working étale locally this lemma reduces to the case of schemes, see Divisors, Lemma 31.13.13. $\square$

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