Timeline for Congruences between CM and non-CM modular forms
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2013 at 3:02 | review | First posts | |||
| Jun 25, 2013 at 8:49 | |||||
| Jun 3, 2013 at 4:03 | comment | added | Orac | @Ventullo: Yes it does (oops). In my defense, the KW-argument I give doesn't require Ihara's Lemma (the proof goes through Taylor's Ihara avoidance), and so generalizes well to higher rank groups. | |
| Jun 3, 2013 at 3:07 | comment | added | Kevin Ventullo | Regarding your extra statement: doesn't this follow already from Ribet's level raising? | |
| Jun 3, 2013 at 2:33 | history | edited | Orac | CC BY-SA 3.0 |
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| Jun 3, 2013 at 2:11 | history | edited | Orac | CC BY-SA 3.0 |
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| Jun 3, 2013 at 2:08 | comment | added | Orac | Dear Noam, exactly correct, although since I'm lazy, it was much easier just to look through the Cremona tables. For comparison, the first four primes which split completely in $\mathbf{Q}(E[3])$ are $61$, $313$, $349$, and $373$. (For some reason, I missed the curve of conductor $1952$ on my first try.) | |
| Jun 3, 2013 at 2:04 | history | edited | Orac | CC BY-SA 3.0 |
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| Jun 3, 2013 at 1:22 | comment | added | Noam D. Elkies | Thanks for the example :-) I suppose that this deformation theory cannot in general produce a rational modular form satisfying the desired congruence, so it was still not clear a priori that you'd find an elliptic curve (as opposed to some more complicated factor of $J_0(N\ell)$ with a subgroup isomorphic to $E[3]$. | |
| Jun 3, 2013 at 1:11 | vote | accept | David Loeffler | ||
| Jun 3, 2013 at 0:04 | history | edited | Orac | CC BY-SA 3.0 |
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| Jun 2, 2013 at 23:38 | history | answered | Orac | CC BY-SA 3.0 |