Lemma 37.22.2. Let f : X \to Y be a morphism of schemes. Assume all fibres of f are locally Noetherian. The following are equivalent
f is Cohen-Macaulay, and
f is flat and its fibres are Cohen-Macaulay schemes.
Lemma 37.22.2. Let f : X \to Y be a morphism of schemes. Assume all fibres of f are locally Noetherian. The following are equivalent
f is Cohen-Macaulay, and
f is flat and its fibres are Cohen-Macaulay schemes.
Proof. This follows directly from the definitions. \square
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