The Stacks project

Remark 59.56.4. Another way to state the conclusion of Theorem 59.56.3 and Fundamental Groups, Lemma 58.2.2 is to say that every sheaf on $\mathop{\mathrm{Spec}}(K)_{\acute{e}tale}$ is representable by a scheme $X$ étale over $\mathop{\mathrm{Spec}}(K)$. This does not mean that every sheaf is representable in the sense of Sites, Definition 7.12.3. The reason is that in our construction of $\mathop{\mathrm{Spec}}(K)_{\acute{e}tale}$ we chose a sufficiently large set of schemes étale over $\mathop{\mathrm{Spec}}(K)$, whereas sheaves on $\mathop{\mathrm{Spec}}(K)_{\acute{e}tale}$ form a proper class.

Comments (0)

There are also:

  • 2 comment(s) on Section 59.56: Galois action on stalks

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Your email address will not be published.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 04JL. Beware of the difference between the letter 'O' and the digit '0'.