Remark 15.87.2. This remark is a continuation of Remark 15.86.5. A sheaf of rings on $\mathbf{N}$ is just an inverse system of rings $(A_ n)$. A sheaf of modules over $(A_ n)$ is exactly the same thing as an object of the category $\textit{Mod}(\mathbf{N}, (A_ n))$ defined above. The derived functor $R\mathop{\mathrm{lim}}\nolimits$ of Lemma 15.87.1 is simply $R\Gamma (\mathbf{N}, -)$ from the derived category of modules to the derived category of modules over the global sections of the structure sheaf. It is true in general that cohomology of groups and modules agree, see Cohomology on Sites, Lemma 21.12.4.

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.

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 091E. Beware of the difference between the letter 'O' and the digit '0'.