Lemma 80.4.2. Let $S$ be a scheme. Let $\mathcal{P}$ be a property as in Definition 80.4.1. Let

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

Lemma 80.4.2. Let $S$ be a scheme. Let $\mathcal{P}$ be a property as in Definition 80.4.1. 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 and has $\mathcal{P}$ so does $a'$.

**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Your email address will not be published.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 (0)