The Stacks project

Remark 15.90.6. While $R \to R_ f$ is always flat, $R \to R^\wedge $ is typically not flat unless $R$ is Noetherian (see Algebra, Lemma 10.97.2 and the discussion in Examples, Section 109.12). Consequently, we cannot in general apply faithfully flat descent as discussed in Descent, Section 35.3 to the morphism $R \to R^\wedge \oplus R_ f$. Moreover, even in the Noetherian case, the usual definition of a descent datum for this morphism refers to the ring $R^\wedge \otimes _ R R^\wedge $, which we will avoid considering in this section.

Comments (0)

There are also:

  • 4 comment(s) on Section 15.90: The Beauville-Laszlo theorem

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Your email address will not be published.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