The Stacks project

Remark 97.6.2. Let $S$ be a locally Noetherian scheme. Let $\mathcal{X}$ be fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Let $k$ be a field of finite type over $S$ and $x_0$ an object of $\mathcal{X}$ over $k$. Let $p : \mathcal{F} \to \mathcal{C}_\Lambda $ be as in ( If $\mathcal{F}$ is a deformation category, i.e., if $\mathcal{F}$ satisfies the Rim-Schlessinger condition (RS), then we see that $\mathcal{F}$ satisfies Schlessinger's conditions (S1) and (S2) by Formal Deformation Theory, Lemma 89.16.6. Let $\overline{\mathcal{F}}$ be the functor of isomorphism classes, see Formal Deformation Theory, Remarks 89.5.2 (10). Then $\overline{\mathcal{F}}$ satisfies (S1) and (S2) as well, see Formal Deformation Theory, Lemma 89.10.5. This holds in particular in the situation of Lemma 97.6.1.

Comments (2)

Comment #2693 by Emanuel Reinecke on

Typo in the second sentence: fppf should be in the subscript

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Your email address will not be published.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