Lemma 48.24.5. If $f : Y \to X$ is a local complete intersection morphism with $X$ a Gorenstein scheme, then $Y$ is Gorenstein.

**Proof.**
By More on Morphisms, Lemma 37.56.5 it suffices to prove the corresponding statement about ring maps. This is Dualizing Complexes, Lemma 47.21.7.
$\square$

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