The Stacks project

Theorem 59.26.4. A ring map $A \to B$ is étale at a prime $\mathfrak q$ if and only if there exists $g \in B$, $g \not\in \mathfrak q$ such that $B_ g$ is standard étale over $A$.

Proof. See Algebra, Proposition 10.144.4. $\square$

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