Lemma 10.130.3. Let k be a field. Let S be a finite type k algebra. The set of Cohen-Macaulay primes forms a dense open U \subset \mathop{\mathrm{Spec}}(S).
Proof. The set is open by Lemma 10.130.2. It contains all minimal primes \mathfrak q \subset S since the local ring at a minimal prime S_{\mathfrak q} has dimension zero and hence is Cohen-Macaulay. \square
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