Lemma 10.146.2. Let $(R, \mathfrak m_ R) \to (S, \mathfrak m_ S)$ be a local homomorphism of local rings. Assume $S$ is the localization of an étale ring extension of $R$. Then there exists a finite, finitely presented, faithfully flat ring map $R \to S'$ such that for every maximal ideal $\mathfrak m'$ of $S'$ there is a factorization

of the ring map $R \to S'_{\mathfrak m'}$.

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