Lemma 23.9.5. Let $A$ be a Noetherian ring. Let $A \to B$ be a finite type ring map. The following are equivalent
$A \to B$ is a local complete intersection in the sense of More on Algebra, Definition 15.33.2,
for every prime $\mathfrak q \subset B$ and with $\mathfrak p = A \cap \mathfrak q$ the ring map $(A_\mathfrak p)^\wedge \to (B_\mathfrak q)^\wedge $ is a complete intersection homomorphism in the sense defined above.