Lemma 76.12.4. In Situation 76.12.1 let $K$ be as in Lemma 76.12.2. Then $K$ is pseudo-coherent relative to $A$.
Proof. Combinging Lemma 76.12.3 and Derived Categories of Spaces, Lemma 74.25.7 we see that $R\Gamma (X, K \otimes ^\mathbf {L} E)$ is pseudo-coherent in $D(A)$ for all pseudo-coherent $E$ in $D(\mathcal{O}_ X)$. Thus the lemma follows from More on Morphisms of Spaces, Lemma 75.51.4. $\square$
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Your email address will not be published.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).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)