Octahedral Galois representations arising from Q-curves of degree 2
| dc.creator | Fernández-González, Julio | |
| dc.creator | Lario, Joan-Carles | |
| dc.creator | Rio, Anna | |
| dc.date | 2001-06-18 | |
| dc.date.accessioned | 2026-07-07T04:42:25Z | |
| dc.date.available | 2026-07-07T04:42:25Z | |
| dc.description | Generically, one can attach to a Q-curve C octahedral representations Gal(Qbar/Q) --> GL(2,Fbar_3) coming from the Galois action on the 3-torsion of those abelian varieties of GL_2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations having image into GL(2,F_9). Going the other way, we can ask which mod 3 octahedral representations of Gal(Qbar/Q) arise from Q-curves in the above sense. We characterize those arising from quadratic Q-curves of degree 2. The approach makes use of Galois embedding techniques in GL(2,F_9), and the characterization can be given in terms of a quartic polynomial defining the S_4-extension of Q attached to the octahedral representation. | |
| dc.identifier | https://arxiv.org/abs/math/0106272 | |
| dc.identifier | http://arxiv.org/abs/math/0106272 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61774 | |
| dc.subject | Number Theory | |
| dc.title | Octahedral Galois representations arising from Q-curves of degree 2 | |
| dc.type | text |