Timeline for varieties with points in number fields
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 18, 2011 at 5:44 | comment | added | Pete L. Clark | @Chris: very true. | |
| Feb 8, 2011 at 16:47 | comment | added | Chris Wuthrich | You won't need BSD: If the analytic rank of the twist of $E$ corresponding to $K$ were zero, then, by Kolyvagin, the rank of this twist would be zero, too. | |
| Feb 4, 2011 at 14:16 | comment | added | Pete L. Clark | @Chris: well, it seems to me that you are imposing one (very mild) additional hypothesis about the $2$-torsion on $E(K)$ and then using some form of BSD to get from the rank to the analytic rank. But notwithstanding those cavils, you have a very nice idea here! I'll think about it and get back to you... | |
| Feb 4, 2011 at 10:52 | comment | added | Chris Wuthrich | If the mod-2 representation of the Jacobian $E$ of $C$ is surjective, then there are no $2$-torsion points on $E(K)$ for quadratic $K$. So the rank of $E$ has to grow in every quadratic $K/\mathbb{Q}$ and so must the analytic rank. But that is not possible by non-vanishing results, I believe. Do I miss something ? | |
| Feb 4, 2011 at 1:34 | vote | accept | Eric Larson | ||
| Feb 4, 2011 at 1:34 | |||||
| Feb 4, 2011 at 1:03 | history | answered | Pete L. Clark | CC BY-SA 2.5 |