Timeline for Congruences between modular forms and the eigencurve construction
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 16, 2015 at 13:59 | vote | accept | user42690 | ||
| Oct 16, 2015 at 6:18 | comment | added | David Loeffler | No, it is much more powerful than just multiplying by Eisenstein series, because it's showing that there are eigenforms of weight $k'$ highly congruent to $f$, not just any old forms of that weight. | |
| Oct 16, 2015 at 3:51 | comment | added | user42690 | And is there no way prove this theorem without constructing the eigencurve? At least if $j=0$ it's just multiplying with the Hasse invariant (Eisenstein series I mean). Maybe I shall post another MO question...... | |
| Oct 16, 2015 at 2:30 | comment | added | user42690 | Thanks, David. It seems that the eignnvariety machine really visualizes properties of modular forms. But this result seems different from the results I know (basically Shimura or Hida's). So is it possible to deduce Shimura's (In A tameness criterion for Galois representations associated to modular forms (mod p) by Gross proposition 9.3 p. 478., Between weight k and weight 2) or Hida's results (between modular forms of same wight I think)? | |
| Oct 15, 2015 at 18:41 | history | answered | David Loeffler | CC BY-SA 3.0 |