On two dimensional weight two odd representations of totally real fields

Details On two dimensional weight two odd representations of totally real fields On two dimensional weight two odd representations of totally real fields

2009-05-26

arxiv.org/abs/0905.4266v1

Mathematics

Number Theory

31 pages

Scientific paper

We say that a two dimensional p-adic Galois representation of a number field F is weight two if it is de Rham with Hodge-Tate weights 0 and -1 equally distributed at each place above p; for example, the Tate module of an elliptic curve has this property. The purpose of this paper is to establish a variety of results concerning odd weight two representations of totally real fields in as great a generality as we are able. Most of these results are improvements upon existing results. Three of our main results are as follows. (1) We prove a modularity lifting theorem for odd weight two representations, extending a theorem of Kisin to include representations which are not potentially crystalline. (2) We show that essentially any odd weight two representation is potentially modular, following the ideas of Taylor. (3) We show that one can lift essentially any odd residual representation to a minimally ramified weight two p-adic representation, using some ideas of Khare-Wintenberger. As an application of these results we show that if rho is a sufficiently irreducible odd weight two p-adic representation of a totally real field F and either F has odd degree or rho is indecomposable at some finite place away from p then rho occurs as the Tate module of a GL_2-type abelian variety. This establishes some new cases of the Fontaine-Mazur conjecture.

Affiliated with

Also associated with

No associations

Rating

On two dimensional weight two odd representations of totally real fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On two dimensional weight two odd representations of totally real fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On two dimensional weight two odd representations of totally real fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-647647