Timeline for Rank of $\mathbb{Z}_{p}$-module $H_{et}^{i}(X,\mathbb{Z}_{p}(r))$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 21, 2022 at 5:25 | comment | added | Sunny | Thanks @gdb for elaborative answer. | |
| Jun 20, 2022 at 21:34 | comment | added | gdb | @Z.M Yep, cohomological dimension of $X_{\overline{K}}$ is $2\mathrm{dim} X$, and cohomological dimension of $G_K$ is 2. | |
| Jun 20, 2022 at 21:31 | comment | added | gdb | @DavidLoeffler Honestly, I just didn't think about it. I am pretty sure it can also be done using the original definition via the formalism of Artin-Rees systems or something along these lines. But I feel that the formalism of derived complete objects is easier to remember. | |
| Jun 20, 2022 at 6:54 | comment | added | David Loeffler | You have introduced a new difinition here (distinct from that of the question) and then shown in the last sentence of Thm 4 that it is equivalent to the original one. Wouldn't it be simpler to work with the original definition throughout? | |
| Jun 20, 2022 at 5:30 | comment | added | Z. M | Do these also imply that $R\Gamma(X,\mathbb Z_\ell)$ (pro-étale) is bounded, therefore coherent? | |
| Jun 20, 2022 at 1:36 | history | answered | gdb | CC BY-SA 4.0 |