The Stacks project

Remark 36.35.12. The reader may have noticed the similarity between Lemma 36.35.11 and Lemma 36.28.3. Indeed, the pseudo-coherent complex $L$ of Lemma 36.35.11 may be characterized as the unique pseudo-coherent complex on $S$ such that there are functorial isomorphisms

\[ \mathop{\mathrm{Ext}}\nolimits ^ i_{\mathcal{O}_ S}(L, \mathcal{F}) \longrightarrow \mathop{\mathrm{Ext}}\nolimits ^ i_{\mathcal{O}_ X}(K, E \otimes _{\mathcal{O}_ X}^\mathbf {L} Lf^*\mathcal{F}) \]

compatible with boundary maps for $\mathcal{F}$ ranging over $\mathit{QCoh}(\mathcal{O}_ S)$. If we ever need this we will formulate a precise result here and give a detailed proof.

Comments (0)

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Your email address will not be published.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



View Remark 36.35.12 as pdf