Lemma 96.9.5 (06W4)—The Stacks project

Loading web-font TeX/Math/Italic

Lemma 96.9.5. Let $p : \mathcal{X} \to (\mathit{Sch}/S)_{fppf}$ be a category fibred in groupoids. Let $\tau \in \{ Zar, {\acute{e}tale}, smooth, syntomic, fppf\}$ . The site $\mathcal{X}_\tau$ has enough points.

Proof. By Sites, Lemma 7.38.5 we have to show that there exists a family of objects $x$ of $\mathcal{X}$ such that $\mathcal{X}_\tau /x$ has enough points and such that the sheaves $h_ x^\#$ cover the final object of the category of sheaves. By Lemma 96.9.1 and Étale Cohomology, Lemma 59.30.1 we see that $\mathcal{X}_\tau /x$ has enough points for every object $x$ and we win. $\square$

Comments (0)

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).

Comments (0)

Post a comment