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The Stacks project

Lemma 23.8.7. Let $A$ be a Noetherian ring. Then $A$ is a local complete intersection if and only if $A_\mathfrak m$ is a complete intersection for every maximal ideal $\mathfrak m$ of $A$.

Proof. This follows immediately from Lemma 23.8.6 and the definitions. $\square$

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