Lemma 29.35.2. Let $f : X \to S$ be a morphism of schemes. Then

1. $f$ is unramified if and only if $f$ is locally of finite type and $\Omega _{X/S} = 0$, and

2. $f$ is G-unramified if and only if $f$ is locally of finite presentation and $\Omega _{X/S} = 0$.

Proof. By definition a ring map $R \to A$ is unramified (resp. G-unramified) if and only if it is of finite type (resp. finite presentation) and $\Omega _{A/R} = 0$. Hence the lemma follows directly from the definitions and Lemma 29.32.5. $\square$

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