The Stacks project

Remark 66.7.3. Here is a list of properties which are local for the étale topology (keep in mind that the fpqc, fppf, syntomic, and smooth topologies are stronger than the étale topology):

1. locally Noetherian, see Descent, Lemma 35.16.1,

2. Jacobson, see Descent, Lemma 35.16.2,

3. locally Noetherian and $(S_ k)$, see Descent, Lemma 35.17.1,

4. Cohen-Macaulay, see Descent, Lemma 35.17.2,

5. Gorenstein, see Duality for Schemes, Lemma 48.24.6,

6. reduced, see Descent, Lemma 35.18.1,

7. normal, see Descent, Lemma 35.18.2,

8. locally Noetherian and $(R_ k)$, see Descent, Lemma 35.18.3,

9. regular, see Descent, Lemma 35.18.4,

10. Nagata, see Descent, Lemma 35.18.5.