Timeline for Does the p-adic Tate module of an elliptic curve with ordinary reduction decompose?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2010 at 19:27 | comment | added | fherzig | It's thm. A.2.4 in Serre's book. | |
| Jun 2, 2010 at 16:37 | comment | added | Martin Orr | Thanks David. I should have found that myself but I didn't realise Serre's book treats the l=p case. | |
| Jun 2, 2010 at 16:37 | vote | accept | Martin Orr | ||
| Jun 2, 2010 at 8:59 | comment | added | David Loeffler | Sorry, typo: I meant $V_p(E)$ (the Tate module tensored up to $\mathbb{Q}_p$), not $V_\ell(E)$. | |
| Jun 2, 2010 at 8:55 | comment | added | David Loeffler | If there was a decomposition $V_\ell(E) = V_1 \oplus V_2$ with $V_i$ stable under (some open subgroup of) the Galois group, then the image of Galois would have to be a p-adic Lie group of dimension at most 2. Since the Borel is 3-dimensional, this isn't the case (the image of Galois is "as large as possible" given that it has to preserve the kernel of reduction). | |
| Jun 2, 2010 at 8:50 | comment | added | Daniel Larsson | David, what do you mean by "Otherwise the image of Galois i open..."? I don't see what this has to do with the conclusion. But I can certainly miss something here. In any case, please enlighten me! | |
| Jun 2, 2010 at 8:31 | history | answered | David Loeffler | CC BY-SA 2.5 |