Lemma 31.23.5. Let $f : X \to Y$ be a morphism of schemes. In each of the following cases pullbacks of meromorphic functions are defined.

every weakly associated point of $X$ maps to a generic point of an irreducible component of $Y$,

$X$, $Y$ are integral and $f$ is dominant,

$X$ is integral and the generic point of $X$ maps to a generic point of an irreducible component of $Y$,

$X$ is reduced and every generic point of every irreducible component of $X$ maps to the generic point of an irreducible component of $Y$,

$X$ is locally Noetherian, and any associated point of $X$ maps to a generic point of an irreducible component of $Y$,

$X$ is locally Noetherian, has no embedded points and any generic point of an irreducible component of $X$ maps to the generic point of an irreducible component of $Y$, and

$f$ is flat.

## Comments (2)

Comment #3770 by Laurent Moret-Bailly on

Comment #3900 by Johan on

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