Timeline for Nontrivial p-divisible groups over $\mathbb Z$ for general prime $p$
Current License: CC BY-SA 4.0
8 events
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| Nov 26, 2018 at 4:39 | comment | added | clever_answer_bot | @ChrisWuthrich No. Vote it down if you want to. As the OP seems to have ignored my answer anyway - which answers the question in a complete a manner as anything available - I have no intention to waste any more effort here looking at this question again. | |
| Nov 26, 2018 at 0:19 | comment | added | Chris Wuthrich | I don't like the tone of the last paragraph. Could you rephrase this, please? | |
| Nov 26, 2018 at 0:12 | history | edited | clever_answer_bot | CC BY-SA 4.0 |
added 3744 characters in body
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| Nov 22, 2018 at 3:53 | comment | added | Zhiyu | "p-DIVISIBLE GROUPS OVER Z" is at iopscience.iop.org/article/10.1070/IM1977v011n05ABEH001752, the section $3$ is short and includes the result of irregular primes. I am a beginner at this area, as there are some citations for those two papers and I am unable to find an Erratum... I apologize if there is any offense, if you like I can remove the words about V. A. Abrashkin's works. I just want to know more about this area, in particular some references for more recent works. | |
| Nov 22, 2018 at 3:37 | comment | added | clever_answer_bot | As I said in my post, the way to prove this is using discriminant bounds. Fontaine's proof that there are no abelian varieties over Z basically is through showing the only 3-divisible groups are the expected ones. | |
| Nov 22, 2018 at 3:37 | comment | added | clever_answer_bot | For $p = 2$ there is of course an extension of $\mathbf{Z}/2 \mathbf{Z}$ by $\mu_2$ as finite flat group schemes defined over $\mathbf{Q}(\sqrt{-1})$, which leads to a $2$-divisible group isogenous to $\mathbf{Q}_2/\mathbf{Z}_2 \oplus \mu_{2^{\infty}}$, but it is still generally conjectured that the only simple finite flat group schemes of $p$-power order are $\mu_p$ and $\mathbf{Z}/p \mathbf{Z}$, which certainly implies Tate's conjecture (up to the one isogeny above when $p=2$). | |
| Nov 21, 2018 at 23:04 | comment | added | Zhiyu | May I ask for some references for the positive results? Thank you. | |
| Nov 21, 2018 at 21:01 | history | answered | clever_answer_bot | CC BY-SA 4.0 |