Timeline for A conjecture of Serre on elliptic curves
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2017 at 9:07 | comment | added | David Loeffler | In contrast to the case of elliptic curves, the Galois representations associated to more general modular forms are very rarely surjective (no matter how large $p$ is): there is an obstruction coming from so-called "inner twists". | |
| Feb 11, 2017 at 9:50 | comment | added | Zakariae.B | Consider all newforms of any weight and any level whose Fourier coefficients lie in the number field $K$. I am asking if there is a prime $p_{K}$ such that for any prime $p>p_{K}$, the $\pmod p$ representations associated to the above newforms ( by the work of P.Deligne ) are all surjective ? | |
| Feb 10, 2017 at 17:37 | comment | added | Jeremy Rouse | This question is somewhat unclear as asked. Are you interested in the problem of fixing a weight $k$, and considering the Galois representations attached to newforms of weight $k$ and asking about their images? Are you interested in restricting the Nebentypus of the modular forms? Are you only interested in representations that land in $GL_{2}(\mathbb{F}_{p})$, which only arise from modular forms $f$ for which there is a degree $1$ prime over $p$ in the ring of integers of the coefficient field? | |
| Feb 10, 2017 at 17:27 | history | asked | Zakariae.B | CC BY-SA 3.0 |