Lemma 29.35.13. Let $f : X \to S$ be a morphism.

If $f$ is unramified, then the diagonal morphism $\Delta : X \to X \times _ S X$ is an open immersion.

If $f$ is locally of finite type and $\Delta $ is an open immersion, then $f$ is unramified.

If $f$ is locally of finite presentation and $\Delta $ is an open immersion, then $f$ is G-unramified.

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