Unramifiedness is a stalk local condition.

Lemma 41.3.2. Let $A \to B$ be of finite type with $A$ a Noetherian ring. Let $\mathfrak q$ be a prime of $B$ lying over $\mathfrak p \subset A$. Then $A \to B$ is unramified at $\mathfrak q$ if and only if $A_{\mathfrak p} \to B_{\mathfrak q}$ is an unramified homomorphism of local rings.

Proof. See discussion above. $\square$

Comment #1090 by Alex Youcis on

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