Timeline for Finite flat group schemes over $\mathbb{Z}$ that are extensions of $\mu_p$ by $\mathbb{Z}/p\mathbb{Z}$
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15 at 21:47 | history | edited | LSpice | CC BY-SA 4.0 |
Link to article, while this is on the front page
|
| Nov 15 at 19:48 | history | edited | Zhiyu | CC BY-SA 4.0 |
added 30 characters in body
|
| Dec 7, 2023 at 18:32 | comment | added | Vik78 | I downvoted since it seems the argument is incomplete. | |
| Sep 10, 2020 at 10:17 | comment | added | Nulhomologous | I am surely confused, but Serre's proof of the result (lemma 3 in section 4.5) only says that Fontaine proved it and no other argument... | |
| Sep 9, 2020 at 17:23 | comment | added | Zhiyu | @Nulhomologous See Serre's Duke87 aghitza.org/pdf/translation-serre-duke.pdf 4.5 Group schemes of type (p, p) over Z, where he uses Fontaine's proof to prove the result for any p>=3. | |
| Sep 9, 2020 at 15:50 | comment | added | Nulhomologous | I am sorry to say that after reading in detail the proof by Fontaine, I must say that he only proves the result for $K=\mathbb{Q}$ and $p=3, 5, 7, 11, 13, 17$ (and for the other fields, for a more restrictive list of primes). This is because he needs his lemma 3.4.2., which in turn uses the tables by Diaz y Diaz only for that primes. I am not sure Abrashkin says something about this problem on some of his papers... | |
| Sep 9, 2020 at 8:42 | vote | accept | Nulhomologous | ||
| Sep 9, 2020 at 0:09 | comment | added | Zhiyu | @Nulhomologous You're right, I forgot to put the "small" restriction. But his method can be improved to give more results, see Abrashkin‘s works. | |
| Sep 9, 2020 at 0:06 | history | edited | Zhiyu | CC BY-SA 4.0 |
added 17 characters in body
|
| Sep 9, 2020 at 0:01 | comment | added | Nulhomologous | Many thanks for the reference. After reading it, it seems to me that Fontaine proved it for $E=\mathbb{Q}, \mathbb{Q}(\sqrt{-1}), \mathbb{Q}(\sqrt{-3})$ and $\mathbb{Q}(\sqrt{5})$ (it needs a more delicate argument for $p=3$ and this last field), not for a general number field... In the result it is under the hypothesis of his theorem 4. | |
| Sep 8, 2020 at 21:42 | history | answered | Zhiyu | CC BY-SA 4.0 |