## 63.2 General remarks

We work in a suitable big fppf site $\mathit{Sch}_{fppf}$ as in Topologies, Definition 34.7.6. So, if not explicitly stated otherwise all schemes will be objects of $\mathit{Sch}_{fppf}$. In Section 63.15 we discuss what changes if you change the big fppf site.

We will always work relative to a base $S$ contained in $\mathit{Sch}_{fppf}$. And we will then work with the big fppf site $(\mathit{Sch}/S)_{fppf}$, see Topologies, Definition 34.7.8. The absolute case can be recovered by taking $S = \mathop{\mathrm{Spec}}(\mathbf{Z})$.

If $U, T$ are schemes over $S$, then we denote $U(T)$ for the set of $T$-valued points *over* $S$. In a formula: $U(T) = \mathop{Mor}\nolimits _ S(T, U)$.

Note that any fpqc covering is a universal effective epimorphism, see Descent, Lemma 35.10.7. Hence the topology on $\mathit{Sch}_{fppf}$ is weaker than the canonical topology and all representable presheaves are sheaves.

## 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Your email address will not be published.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.

## Comments (2)

Comment #2658 by Raymond Cheng on

Comment #2674 by Johan on