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- W2950480014 abstract "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." @default.
- W2950480014 created "2019-06-27" @default.
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- W2950480014 date "1999-01-18" @default.
- W2950480014 modified "2023-10-18" @default.
- W2950480014 title "Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations" @default.
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