Lemma 15.116.9. Let $A \to B$ be an extension of discrete valuation rings with fraction fields $K \subset L$. Assume

$B$ is essentially of finite type over $A$,

either $A$ or $B$ is a Nagata ring, and

$L/K$ is separable.

Then there exists a separable solution for $A \to B$ (Definition 15.115.1).

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