Timeline for Automorphic representations attached to abelian varieties
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Jul 13, 2010 at 14:11 | comment | added | user2490 | I think that you may want automorphic forms on GSpin(2d+1)/Q (split with root datum dual to that of GSp(2d)) and not on Spin(2d+1)/Q (split with root datum dual to that of PSp(2d)), unless you are projectivizing your Galois representations (into PSp(2d) instead of GSp(2d)). I don't follow your remark about the multiplicity of spin groups. The most general place to imagine your automorphic forms is on the (unique) split reductive group over Q with the described root datum. You may be able to transfer to an inner form over Q, depending on ramification. | |
| Jul 13, 2010 at 2:00 | comment | added | David Hansen | @james-parson: Yes, I believe you are right, and I should have used spin groups - but even still, there are many R-split spin groups of a given dimension. | |
| Jul 13, 2010 at 1:57 | comment | added | user2490 | Don't you intend to use automorphic forms on something whose dual group is GSp(2d)? I think one would usually write GSpin(2d + 1)/Q for the split group over Q with the appropriate root datum. Since the Galois representations associated to you abelian variety A/Q are representations (and not cocycles), one would expect an automorphic form on GSpin(2d + 1)/Q (and not an outer form). I don't know whether one would expect to be able to transfer to some inner form G/Q that is not split at R, but perhaps you are not worried about that. | |
| Jul 13, 2010 at 1:54 | comment | added | David Hansen | (whoops) - so, yes, I am using functoriality. :) | |
| Jul 13, 2010 at 1:51 | comment | added | David Hansen | The Galois representation attached to $T_\ell(A)$ has image in $Sp_{2d}(\overline{\mathbb{Q}_{\ell}})$, and $Sp_{2d}$ is the dual group of $SO(2d+1)$. | |
| Jul 13, 2010 at 0:18 | comment | added | Victor Protsak | Are you using Langlands functoriality to lift these automorphic representations? I understand how to pass from abelian variety to $Sp(2d)$ to $GL(2d)$, but what is your connection with orthogonal group? (Liberally insert conjectural(ly) throughout.) | |
| Jul 12, 2010 at 18:43 | history | asked | David Hansen | CC BY-SA 2.5 |