Lemma 71.6.12 (0840)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 71: Divisors on Algebraic Spaces
Section 71.6: Effective Cartier divisors
Lemma 71.6.12 (cite)

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Lemma 71.6.12. Let $S$ be a scheme. Let $f : X' \to X$ be a morphism of algebraic spaces over $S$ . Let $D_1$ , $D_2$ be effective Cartier divisors on $X$ . If the pullbacks of $D_1$ and $D_2$ are defined then the pullback of $D = D_1 + D_2$ is defined and $f^*D = f^*D_1 + f^*D_2$ .

Proof. Omitted. $\square$

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