Lemma 48.25.3 (0C05)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 48: Duality for Schemes
Section 48.25: Gorenstein morphisms
Lemma 48.25.3 (cite)

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Lemma 48.25.3. Let $f : X \to Y$ be a morphism of schemes. Assume all fibres of $f$ are locally Noetherian. The following are equivalent

$f$ is Gorenstein, and
$f$ is flat and its fibres are Gorenstein schemes.

Proof. This follows directly from the definitions. $\square$

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