The Stacks project

Lemma 71.10.7. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Pullbacks of meromorphic sections are defined in each of the following cases

  1. weakly associated points of $X$ are mapped to points of codimension $0$ on $Y$,

  2. $f$ is flat,

  3. add more here as needed.

Proof. Working ├ętale locally, this translates into the case of schemes, see Divisors, Lemma 31.23.5. To do the translation use Lemma 71.7.5 (description of regular sections), Definition 71.2.2 (definition of weakly associated points), and Properties of Spaces, Lemma 66.11.1 (description of codimension $0$ points). $\square$

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