Lemma 10.104.9. Let $R$ be a local Noetherian Cohen-Macaulay ring of dimension $d$. Let $M$ be a finite $R$ module of depth $e$. There exists an exact complex

$0 \to K \to F_{d-e-1} \to \ldots \to F_0 \to M \to 0$

with each $F_ i$ finite free and $K$ maximal Cohen-Macaulay.

Proof. Immediate from the definition and Lemma 10.104.8. $\square$

There are also:

• 7 comment(s) on Section 10.104: Cohen-Macaulay rings

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).