The Stacks project

Proposition 59.106.2. Let $K$ be an object of $D^+((\mathit{Sch}/S)_{fppf})$. Then $K$ is in the essential image of $R\epsilon _* : D((\mathit{Sch}/S)_ h) \to D((\mathit{Sch}/S)_{fppf})$ if and only if $c^ K_{X, X', Z, E}$ is a quasi-isomorphism for every almost blow up square (59.106.0.1) in $(\mathit{Sch}/S)_ h$ with $X$ affine.

Proof. We prove this by applying Cohomology on Sites, Lemma 21.29.2 whose hypotheses hold by Lemma 59.106.1 and More on Flatness, Proposition 38.37.9. $\square$

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Your email address will not be published.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



View Proposition 59.106.2 as pdf