Lemma 27.13.8. Let $X$ be a scheme. The following are equivalent:

$X$ is Nagata, and

$X$ is locally Noetherian and universally Japanese.

Lemma 27.13.8. Let $X$ be a scheme. The following are equivalent:

$X$ is Nagata, and

$X$ is locally Noetherian and universally Japanese.

**Proof.**
This is Algebra, Proposition 10.156.15.
$\square$

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