Proposition 41.19.3. Let A, B be Noetherian local rings. Let f : A \to B be an étale homomorphism of local rings. Then A is Cohen-Macaulay if and only if B is so.
Being Cohen-Macaulay ascends and descends along étale maps.
Proof. A local ring A is Cohen-Macaulay if and only if \dim (A) = \text{depth}(A). As both of these invariants is preserved under an étale extension, the claim follows. \square
Comments (1)
Comment #985 by Johan Commelin on