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Both "Residues and duality" and The stacks project do not agree with this definition (both say a scheme is Gorenstein if all of its local rings are Gorenstein). Who is right?

Thank you for the info. I checked the stack project and they require a Gorenstein scheme to be Cohen-Macaulay (this requirement is undesirable since it would be consistent with Q-Gorenstein,) I have added a note to the article. -- Taku ( talk) 21:24, 19 December 2015 (UTC) reply