Lemma 26.14.2. In Lemma 26.14.1 above, assume that all $X_ i$ are schemes. Then the resulting locally ringed space $X$ is a scheme.

** Schemes can be glued to give new schemes. **

**Proof.**
This is clear since each of the $U_ i$ is a scheme and hence every $x \in X$ has an affine neighbourhood.
$\square$

## 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Your email address will not be published.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).

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 #840 by Johan Commelin on

There are also: