The Stacks project

Lemma 37.62.15. Let $f : X \to Y$ be a local complete intersection homomorphism. Then the naive cotangent complex $\mathop{N\! L}\nolimits _{X/Y}$ is a perfect object of $D(\mathcal{O}_ X)$ of tor-amplitude in $[-1, 0]$.

Proof. Translated into algebra this is More on Algebra, Lemma 15.85.4. To do the translation use Lemmas 37.62.5 and 37.13.2 as well as Derived Categories of Schemes, Lemmas 36.3.5, 36.10.4 and 36.10.7. $\square$

Comments (0)

There are also:

  • 4 comment(s) on Section 37.62: Local complete intersection morphisms

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Your email address will not be published.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 0FV6. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 37.62.15 as pdf