Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

Details Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

1999-01-18

arxiv.org/abs/math/9901156v1

Mathematics

Number Theory

Scientific paper

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".

Affiliated with

Also associated with

No associations

Rating

Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations 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 Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-311346