Lemma 80.3.3 (03Y0)—The Stacks project

Processing math: 100%

Table of contents
Part 4: Algebraic Spaces
Chapter 80: Bootstrap
Section 80.3: Morphisms representable by algebraic spaces
Lemma 80.3.3 (cite)

previous lemma
next lemma

numberstags

history
statistics
4 tags refer to this tag

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

Lemma 80.3.3. 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. $\square$

Comments (1)

Comment #894 by Kestutis Cesnavicius on August 09, 2014 at 13:02

Suggested slogan: A base change of a representable by algebraic spaces morphism of presheaves is representable by algebraic spaces

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 (1)

Post a comment