Lemma 47.17.1. Let $A$ be a Noetherian ring. Let $\mathfrak p$ be a minimal prime of $A$. Then $H^ i(\omega _ A^\bullet )_\mathfrak p$ is nonzero for exactly one $i$.
Proof. The complex $\omega _ A^\bullet \otimes _ A A_\mathfrak p$ is a dualizing complex for $A_\mathfrak p$ (Lemma 47.15.6). The dimension of $A_\mathfrak p$ is zero as $\mathfrak p$ is minimal. Hence the result follows from Lemma 47.16.8. $\square$
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like
$\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.