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The Stacks project

Definition 76.27.2. Let S be a scheme. Let f : X \to Y be a morphism of algebraic spaces over S. Assume the fibres of f are locally Noetherian (Divisors on Spaces, Definition 71.4.2).

  1. Let x \in |X|, and y = f(x). We say that f is Gorenstein at x if f is flat at x and the equivalent conditions of Morphisms of Spaces, Lemma 67.22.5 hold for the property \mathcal{P} described in Lemma 76.27.1.

  2. We say f is a Gorenstein morphism if f is Gorenstein at every point of X.


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