Lemma 79.3.3. Let $S$ be a scheme. Let

be a fibre square of presheaves on $(\mathit{Sch}/S)_{fppf}$. If $a$ is representable by algebraic spaces so is $a'$.

** A base change of a representable by algebraic spaces morphism of presheaves is representable by algebraic spaces. **

Lemma 79.3.3. Let $S$ be a scheme. Let

\[ \xymatrix{ G' \times _ G F \ar[r] \ar[d]^{a'} & F \ar[d]^ a \\ G' \ar[r] & G } \]

be a fibre square of presheaves on $(\mathit{Sch}/S)_{fppf}$. If $a$ is representable by algebraic spaces so is $a'$.

**Proof.**
Omitted. Hint: This is formal.
$\square$

Your email address will not be published.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 (1)

Comment #894 by Kestutis Cesnavicius on