The Stacks project

Definition 97.13.1. Let $S$ be a locally Noetherian scheme.

  1. Let $\mathcal{X}$ be a category fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. We say $\mathcal{X}$ satisfies openness of versality if given a scheme $U$ locally of finite type over $S$, an object $x$ of $\mathcal{X}$ over $U$, and a finite type point $u_0 \in U$ such that $x$ is versal at $u_0$, then there exists an open neighbourhood $u_0 \in U' \subset U$ such that $x$ is versal at every finite type point of $U'$.

  2. Let $f : \mathcal{X} \to \mathcal{Y}$ be a $1$-morphism of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. We say $f$ satisfies openness of versality if given a scheme $U$ locally of finite type over $S$, an object $y$ of $\mathcal{Y}$ over $U$, openness of versality holds for $(\mathit{Sch}/U)_{fppf} \times _\mathcal {Y} \mathcal{X}$.


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Your email address will not be published.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 07XQ. Beware of the difference between the letter 'O' and the digit '0'.