The Stacks project

Lemma 60.12.2. Let $(T, \mathcal{J}, \delta )$ be a divided power scheme. Let $T \to S$ be a morphism of schemes. The quotient $\Omega _{T/S} \to \Omega _{T/S, \delta }$ described above is a quasi-coherent $\mathcal{O}_ T$-module. For $W \subset T$ affine open mapping into $V \subset S$ affine open we have

\[ \Gamma (W, \Omega _{T/S, \delta }) = \Omega _{\Gamma (W, \mathcal{O}_ W)/\Gamma (V, \mathcal{O}_ V), \delta } \]

where the right hand side is as constructed in Section 60.6.

Proof. Omitted. $\square$

Comments (0)

There are also:

  • 2 comment(s) on Section 60.12: Sheaf of differentials

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Your email address will not be published.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 07IY. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 60.12.2 as pdf