Lemma 61.3.2. Let $A \to B$ and $A \to A'$ be ring maps. Let $B' = B \otimes _ A A'$ be the base change of $B$.

If $A \to B$ is a local isomorphism, then $A' \to B'$ is a local isomorphism.

If $A \to B$ identifies local rings, then $A' \to B'$ identifies local rings.

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