The Stacks project

Lemma 33.16.6. Let $f : X \to Y$ be a morphism of schemes over a base scheme $S$. Let $x \in X$ be a point. Set $y = f(x)$. If $\kappa (y) = \kappa (x)$, then $f$ induces a natural linear map

\[ \text{d}f : T_{X/S, x} \longrightarrow T_{Y/S, y} \]

which is dual to the linear map $\Omega _{Y/S, y} \otimes \kappa (y) \to \Omega _{X/S, x}$ via the identifications of Lemma 33.16.4.

Proof. Omitted. $\square$


Comments (3)

Comment #3268 by Dario Weißmann on

Typo: after the map df there is a point but the sentence is not yet finished

Comment #3271 by Dario Weißmann on

Also should be replaced by .


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Your email address will not be published.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 0B2F. Beware of the difference between the letter 'O' and the digit '0'.