Timeline for mod p etale cohomology of the special fiber and the generic fiber
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 29, 2018 at 2:41 | comment | added | Boa | Good point. I removed the wrong answer, and failed to find a correct answer. | |
| Sep 29, 2018 at 2:41 | history | edited | Boa | CC BY-SA 4.0 |
removed incorrect answer
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| Sep 29, 2018 at 1:28 | comment | added | Zhiyu | While the argument is clever, and you get that the special fiber's etale cohomology can be controlled by the de Rham cohomology in special fiber, buy how do you control the latter term by the etale cohomology of the generic fiber? (BMS is for the opposite direction) | |
| Sep 29, 2018 at 1:23 | comment | added | Zhiyu | @R.vanDobbendeBruyn By a semilinear lemma 0A3L the Artin-Schreier long exact sequence splits, see stacks.math.columbia.edu/tag/0A3J | |
| Sep 29, 2018 at 0:49 | comment | added | R. van Dobben de Bruyn | Why does Artin-Schreier theory imply that $H^i(Y,\mathbb F_p) \otimes_{\mathbb F_p} k \to H^i(Y,\mathcal O_Y)$ is injective? I guess I don't understand how $\operatorname{id} - \operatorname{Frob}$ acts on $H^i(Y,\mathcal O_Y)$ (although the $-\otimes_{\mathbb F_p} k$ step also feels dangerous). | |
| Sep 29, 2018 at 0:10 | history | answered | Boa | CC BY-SA 4.0 |