Lemma 94.9.5. Let $S$ be an object of $\mathit{Sch}_{fppf}$. Let $a : F \to G$ be a map of presheaves of sets on $(\mathit{Sch}/S)_{fppf}$. Denote $a' : \mathcal{S}_ F \to \mathcal{S}_ G$ the associated map of categories fibred in sets. Then $a$ is representable by algebraic spaces (see Bootstrap, Definition 80.3.1) if and only if $a'$ is representable by algebraic spaces.
Proof. Omitted. $\square$
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Your email address will not be published.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)
There are also: