Lemma 23.8.9. Let $A \to B$ be a flat local homomorphism of Noetherian local rings. Then the following are equivalent
$B$ is a complete intersection,
$A$ and $B/\mathfrak m_ A B$ are complete intersections.
Lemma 23.8.9. Let $A \to B$ be a flat local homomorphism of Noetherian local rings. Then the following are equivalent
$B$ is a complete intersection,
$A$ and $B/\mathfrak m_ A B$ are complete intersections.
Proof. Now that the definition makes sense this is a trivial reformulation of the (nontrivial) Proposition 23.8.4. $\square$
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