Processing math: 0%

The Stacks project

Lemma 34.9.9. Let T be an affine scheme. Let \{ T_ i \to T\} _{i \in I} be an fpqc covering of T. Then there exists an fpqc covering \{ U_ j \to T\} _{j = 1, \ldots , n} which is a refinement of \{ T_ i \to T\} _{i \in I} such that each U_ j is an affine scheme. Moreover, we may choose each U_ j to be open affine in one of the T_ i.

Proof. This follows directly from the definition. \square

Comments (0)

There are also:

  • 8 comment(s) on Section 34.9: The fpqc topology

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Your email address will not be published.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 022E. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 34.9.9 as pdf