The Stacks project

Lemma 95.6.1. The functor

\[ p : \textit{FÉt} \longrightarrow (\mathit{Sch}/S)_{fppf} \]

defines a stack over $(\mathit{Sch}/S)_{fppf}$.

Proof. Fppf descent for finite étale morphisms follows from Descent, Lemmas 35.37.1, 35.23.23, and 35.23.29. Details omitted. $\square$

Comments (2)

Comment #6272 by Owen on

'stack in groupoids' -> this is not true since the fiber categories are not groupoids.

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Your email address will not be published.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


View Lemma 95.6.1 as pdf