Lemma 35.17.2. The property $\mathcal{P}(S) =$“$S$ is Cohen-Macaulay” is local in the syntomic topology.

**Proof.**
This is clear from Lemma 35.17.1 above since a scheme is Cohen-Macaulay if and only if it is locally Noetherian and $(S_ k)$ for all $k \geq 0$, see Properties, Lemma 28.12.3.
$\square$

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