Lemma 84.8.6. Let $\mathcal{C}$ be as in Situation 84.3.3. Let $U \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C}_ n)$. Let $\mathcal{F} \in \textit{Ab}(\mathcal{C}_{total})$. Then $H^ p(U, \mathcal{F}) = H^ p(U, g_ n^{-1}\mathcal{F})$ where on the left hand side $U$ is viewed as an object of $\mathcal{C}_{total}$.

**Proof.**
Observe that “$U$ viewed as object of $\mathcal{C}_{total}$” is explained by the construction of $\mathcal{C}_{total}$ in Lemma 84.3.1 in case (A) and Lemma 84.3.2 in case (B). The equality then follows from Lemma 84.3.6 and the definition of cohomology.
$\square$

## 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Your email address will not be published.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).

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)