Lemma 96.9.4. Let $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ be a category fibred in groupoids. Let $\tau \in \{ Zar, {\acute{e}tale}, smooth, syntomic, fppf\} $. Let $x \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{X})$ lying over $U = p(x)$. The equivalence of Lemma 96.9.1 extends to an equivalence of ringed sites $(\mathcal{X}_\tau /x, \mathcal{O}_\mathcal {X}|_ x) \to ((\mathit{Sch}/U)_\tau , \mathcal{O})$.
Proof. This is immediate from the construction of the structure sheaves. $\square$
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)