The Stacks project

Lemma 39.12.2. Let $S$ be a scheme. Let $G$ be a group scheme over $S$. Let $f : Y \to X$ be a $G$-equivariant morphism between $S$-schemes endowed with $G$-actions. Then pullback $f^*$ given by $(\mathcal{F}, \alpha ) \mapsto (f^*\mathcal{F}, (1_ G \times f)^*\alpha )$ defines a functor from the category of $G$-equivariant quasi-coherent $\mathcal{O}_ X$-modules to the category of $G$-equivariant quasi-coherent $\mathcal{O}_ Y$-modules.

Proof. Omitted. $\square$

Comments (2)

Comment #4284 by Laurent Moret-Bailly on

Statement of lemma: why is "quasi-coherent" omitted on the side?

There are also:

  • 12 comment(s) on Section 39.12: Equivariant quasi-coherent sheaves

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Your email address will not be published.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 03LG. Beware of the difference between the letter 'O' and the digit '0'.