Lemma 23.9.4. Consider a commutative diagram
\xymatrix{ S \ar[r] & B \\ & A \ar[lu] \ar[u] }
of Noetherian local rings with S \to B surjective, A \to S flat, and S/\mathfrak m_ A S a regular local ring. The following are equivalent
\mathop{\mathrm{Ker}}(S \to B) is generated by a regular sequence, and
A^\wedge \to B^\wedge is a complete intersection homomorphism as defined above.
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