The Stacks project

Remark 37.44.8. As a consequence of Lemma 37.44.7 we obtain a comparison morphism

\[ \epsilon : (\mathit{Sch}/S)_{ph} \longrightarrow (\mathit{Sch}/S)_{fppf} \]

This is the morphism of sites given by the identity functor on underlying categories (with suitable choices of sites as in Topologies, Remark 34.11.1). The functor $\epsilon _*$ is the identity on underlying presheaves and the functor $\epsilon ^{-1}$ associated to an fppf sheaf its ph sheafification. By composition we can in addition compare the ph topology with the syntomic, smooth, ├ętale, and Zariski topologies.


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Your email address will not be published.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