Lemma 29.52.1. Let $S$ be a scheme. Let $f : X \to S$ be a morphism of schemes. Let $x \in X$, and set $s = f(x)$. Assume

$S$ is locally Noetherian,

$f$ is locally of finite type,

$X$ and $S$ integral, and

$f$ dominant.

We have

Moreover, equality holds if $S$ is universally catenary.

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