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 $X$.

Comments (0)

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 0E14. Beware of the difference between the letter 'O' and the digit '0'.



View Definition 76.27.2 as pdf