The Stacks project

Lemma 114.14.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $X = \bigcup _{j \in J} X_ j$ be a Zariski covering, see Spaces, Definition 64.12.5. If each $X_ j$ satisfies the sheaf property for the fpqc topology then $X$ satisfies the sheaf property for the fpqc topology.

Proof. This is true because all algebraic spaces satisfy the sheaf property for the fpqc topology, see Properties of Spaces, Proposition 65.17.1. $\square$


Comments (0)


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Your email address will not be published.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.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 03WA. Beware of the difference between the letter 'O' and the digit '0'.