The Stacks project

Exercise 111.35.5. Let $f : X \to S$ be a morphism of schemes. Let $x \in X$. Define addition of tangent vectors, using Exercise 111.35.4 and a suitable morphism

\[ \mathop{\mathrm{Spec}}(K[\epsilon ]) \longrightarrow \mathop{\mathrm{Spec}}(K[\epsilon _1, \epsilon _2]/(\epsilon _1\epsilon _2)). \]

Similarly, define scalar multiplication of tangent vectors (this is easier). Show that $T_{X/S, x}$ becomes a $\kappa (x)$-vector space with your constructions.


Comments (0)

There are also:

  • 3 comment(s) on Section 111.35: Tangent Spaces

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Your email address will not be published.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 029H. Beware of the difference between the letter 'O' and the digit '0'.