Proposition 36.7.5. Let $X$ be a quasi-compact scheme with affine diagonal. Then the functor (36.3.0.1)

is an equivalence with quasi-inverse given by $RQ_ X$.

Proposition 36.7.5. Let $X$ be a quasi-compact scheme with affine diagonal. Then the functor (36.3.0.1)

\[ D(\mathit{QCoh}(\mathcal{O}_ X)) \longrightarrow D_\mathit{QCoh}(\mathcal{O}_ X) \]

is an equivalence with quasi-inverse given by $RQ_ X$.

**Proof.**
Let $U \subset X$ be an affine open. Then the morphism $U \to X$ is affine by Morphisms, Lemma 29.11.11. Thus the assumption of Lemma 36.7.4 holds by Lemma 36.7.1 and we win.
$\square$

Your email address will not be published.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.

## Comments (0)