Timeline for Galois representation attached to elliptic curves
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2010 at 4:36 | vote | accept | Arijit | ||
| Jun 25, 2010 at 4:36 | comment | added | Arijit | Oh I am being really very careless. I briefly looked at the paper. But it doesnt say anything about the abelian variety that corresponds to the modular form. I believe that it is not a very appropriate question because my knowledge in this field is really very limited. Thanks again Prof. Emerton for clarifying my doubts. | |
| Jun 25, 2010 at 4:08 | comment | added | Emerton | By "coming from a modular form", do you mean "modular form of weight 2 and trivial nebentypus"? In general, the Galois rep. coming from a modular form of weight k and nebentypus epsilon has determinant cyclotomic^(k-1) epsilon (or the inverse of this, depending on conventions). Also, "doesn't come from a modular form" should probably read "doesn't come from an elliptic curve". | |
| Jun 25, 2010 at 3:55 | comment | added | Arijit | Ok I should have added that. I am assuming that the Galois representation is coming from a modular form so the determinant already has cyclotomic character. As for the example for p=7 there is indeed a form of level 29 and weight 2 whose mod 7 Galois representation doesnt come from a modular form. So that got me thinking what went wrong for that prime. As you have pointed out the condition is not sufficient for higher primes, that raises the natural question about the arithmetic of these representations. Anyway thanks a lot for your answer. I will look into Calegari's paper | |
| Jun 25, 2010 at 3:49 | history | answered | Emerton | CC BY-SA 2.5 |