The Stacks project

Lemma 69.8.3. Let $S$ be a scheme. Let $f : X \to Y$ be an affine morphism of algebraic spaces over $S$. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. Then $H^ i(X, \mathcal{F}) = H^ i(Y, f_*\mathcal{F})$ for all $i \geq 0$.

Proof. Follows from Lemma 69.8.2 and the Leray spectral sequence. See Cohomology on Sites, Lemma 21.14.6. $\square$

Comments (2)

Comment #5517 by Shend Zhjeqi on

I might be mistaken but shouldn't the second cohomology( in lemma 67.8.3) be over and not over . I.e. instead of
should we have

Thank you.

Feel free to delete the comment afterwards.

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Your email address will not be published.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 0D2U. Beware of the difference between the letter 'O' and the digit '0'.