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.