The Stacks project

Theorem 64.20.1 (Finite Coefficients). Let $X$ be a scheme of finite type over a finite field $k$. Let $\Lambda $ be a finite ring of order prime to the characteristic of $k$ and $\mathcal{F}$ a constructible flat $\Lambda $-module on $X_{\acute{e}tale}$. Then

\[ L(X, \mathcal{F}) = \det (1 - \pi _ X^*\ T |_{R\Gamma _ c(X_{\bar k}, \mathcal{F})})^{-1} \in \Lambda [[T]]. \]

Proof. Omitted. $\square$

Comments (0)

There are also:

  • 2 comment(s) on Section 64.20: Cohomological interpretation

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Your email address will not be published.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 03UZ. Beware of the difference between the letter 'O' and the digit '0'.



View Theorem 64.20.1 as pdf