Lifting systems of Galois representations associated to abelian varieties
| dc.creator | Noot, Rutger | |
| dc.date | 2004-07-21 | |
| dc.date | 2006-12-30 | |
| dc.date.accessioned | 2026-07-07T07:37:33Z | |
| dc.date.available | 2026-07-07T07:37:33Z | |
| dc.description | This paper treats what we call `weak geometric liftings' of Galois representations associated to abelian varieties. This notion can be seen as a generalization of the idea of lifting a Galois representation along an isogeny of algebraic groups. The weaker notion only takes into account an isogeny of the derived groups and disregards the centres of the groups in question. The weakly lifted representations are required to be geometric in the sense of a conjecture of Fontaine and Mazur. The conjecture in question states that any irreducible geometric representation is a twist of a subquotient of an étale cohomology group of an algebraic variety over a number field. It is shown that a Galois representation associated to an abelian variety admits a weak geometric lift to a group with simply connected derived group. In certain cases, such a weak geometric lift is itself associated to an abelian variety. This means that the conjecture of Fontaine and Mazur is confirmed for these representations. In other cases, one may find a lift which can not be found back in the etale cohomology of any abelian variety. The Fontaine--Mazur conjecture remains open for these representations. Nevertheless, certain consequences of the conjecture can be established. | |
| dc.description | 50 pages. In version 3 some clarifications and examples are added, some proofs streamlined. Except for the layout, this version coincides with the published paper | |
| dc.identifier | https://arxiv.org/abs/math/0407360 | |
| dc.identifier | http://arxiv.org/abs/math/0407360 | |
| dc.identifier | Journal of the Ramanujan Mathematical Society, 21 No. 4 (2006), pp. 299-342 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120813 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G10; 11F80; 14K15 | |
| dc.title | Lifting systems of Galois representations associated to abelian varieties | |
| dc.type | text |