Theorem 41.12.2. Let $f : A \to B$ be an unramified morphism of local rings. Then there exist $f, g \in A[t]$ such that

$B' = A[t]_ g/(f)$ is standard étale – see (a) and (b) above, and

$B$ is isomorphic to a quotient of a localization of $B'$ at a prime.

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