The Stacks project

Lemma 77.3.7. Let $S$ be a scheme. Let $a : F \to G$ be a map of presheaves on $(\mathit{Sch}/S)_{fppf}$. Suppose $a : F \to G$ is representable by algebraic spaces. If $X$ is an algebraic space over $S$, and $X \to G$ is a map of presheaves then $X \times _ G F$ is an algebraic space.

Proof. By Lemma 77.3.3 the transformation $X \times _ G F \to X$ is representable by algebraic spaces. Hence it is an algebraic space by Lemma 77.3.6. $\square$


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Your email address will not be published.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