Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
| dc.creator | Tilouine, Jacques | |
| dc.creator | Urban, Eric | |
| dc.date | 1999-01-18 | |
| dc.date.accessioned | 2026-07-07T05:27:43Z | |
| dc.date.available | 2026-07-07T05:27:43Z | |
| dc.description | Let F be a totally real field and G=GSp(4)_{/F}. In this paper, we show under a weak assumption that, given a Hecke eigensystem lambda which is (p,P)-ordinary for a fixed parabolic P in G, there exists a several variable p-adic family underline{lambda} of Hecke eigensystems (all of them (p,P)-nearly ordinary) which contains lambda. The assumption is that lambda is cohomological for a regular coefficient system. If F=Q, the number of variables is three. Moreover, in this case, we construct the three variable p-adic family rho_{underline{lambda}} of Galois representations associated to underline{lambda}. Finally, under geometric assumptions (which would be satisfied if one proved that the Galois representations in the family come from Grothendieck motives), we show that rho_{underline{lambda}} is nearly ordinary for the dual parabolic of P. This text is an updated version of our first preprint (issued in the "Prepublication de l'universite Paris-Nord") and will appear in the "Annales Scientifiques de l' E N S". | |
| dc.identifier | https://arxiv.org/abs/math/9901156 | |
| dc.identifier | http://arxiv.org/abs/math/9901156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78024 | |
| dc.subject | Number Theory | |
| dc.title | Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations | |
| dc.type | text |