Corollary

Tag 0D50, permanent. Cite it as [Bourbaki, Tag 0D50].

Let $A$ be a noetherian local ring of dimension d. The $A$ -module $\operatorname{Ext}^d_A(\kappa_A, A)$ is not zero.

This follows from th. 2 if $A$ is a Gorenstein ring and from lemma 2 otherwise.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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