Timeline for What is the first cohomology $H_{fppf}^{1}(X, \alpha_{p})$?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| May 6 at 7:33 | comment | added | Niels | Actually, what I wrote is wrong, interstingly. My reference was J.Milne's article "Abelian varieties" in the yellow book "Arithmetic geometry" doi.org/10.1007/978-1-4613-8655-1, precisely Remark 8.5 p.116-117. But I discovered some years ago and to my great suprise that this turns out to be false. The local-local term can be more complicated. Thanks for S.Mehidi for pointing out recently this wrong post and the counter-example in Rachel Pries article [[math/0609658] A short guide to p-torsion of abelian varieties in characteristic p](arxiv.org/abs/math/0609658) Example 2.2. | |
| Jan 1, 2016 at 8:59 | comment | added | kiseki | @Niels: So, $(\mathbb{Z}/p\mathbb{Z})^{2(g-r)}$ ? | |
| Jan 1, 2016 at 8:48 | answer | added | R. van Dobben de Bruyn | timeline score: 17 | |
| Jan 1, 2016 at 8:47 | comment | added | Niels | And since $\operatorname{Pic}_{X/k}[p]\simeq \left( \mathbb Z /p \right)^h \times \left(\mu_p\right)^h \times \left(\alpha_p\right)^{2(g-h)}$, where $h$ is the $p$-rank, if I am correct, we are almost done. | |
| Jan 1, 2016 at 8:39 | comment | added | Jason Starr | By Cartier duality, $H^1_{fppf}(X,\alpha_p)$ should be the same as the group of morphisms of group schemes $\alpha_p\to \text{Pic}_{X/k}$. | |
| S Jan 1, 2016 at 8:16 | history | suggested | R. van Dobben de Bruyn | CC BY-SA 3.0 |
Fixed a small mistake
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| Jan 1, 2016 at 8:05 | review | Suggested edits | |||
| S Jan 1, 2016 at 8:16 | |||||
| Jan 1, 2016 at 7:38 | history | asked | kiseki | CC BY-SA 3.0 |