Timeline for Computing (on a computer) higher ramification groups and/or conductors of representations.
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 10, 2011 at 3:59 | comment | added | Junkie | The latest Magma does this trivially in 0.6s and 25MB, so they must have improved it. | |
| Dec 16, 2010 at 22:40 | answer | added | Lubin | timeline score: 38 | |
| Mar 6, 2010 at 20:24 | vote | accept | Kevin Buzzard | ||
| Mar 6, 2010 at 10:04 | answer | added | David Loeffler | timeline score: 29 | |
| Mar 5, 2010 at 22:37 | comment | added | moonface | Quick ad hoc calculation (not checked): standard permutation representation of D_8 on a square gives a 4-dimensional linear representation, which is the sum of a trivial representation, the representation you want, and a quadratic character. The discriminant of the associated quartic field is (at 2) of valuation 10, so you just need to figure out what the associated quadratic field is; I think (without checking) it's $\mathbb{Q}(\sqrt{2})$, so that gives 7. Did that very hastily, though, don't trust i | |
| Mar 5, 2010 at 20:32 | comment | added | Kevin Buzzard | Somehow I suspect (although I didn't check) that although you are right, these limitations will somehow be built in to the standard limitations on the jumps explained in e.g. Serre's local fields book. | |
| Mar 5, 2010 at 20:12 | answer | added | dke | timeline score: 9 | |
| Mar 5, 2010 at 19:58 | comment | added | Marty | Have you considered the constraints imposed by the integrality of the Artin conductor? For 2-dimensional Galois representations of dihedral type, I'd think this would limit the possibilities for higher ramification groups. | |
| Mar 5, 2010 at 19:34 | history | asked | Kevin Buzzard | CC BY-SA 2.5 |