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

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          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".

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          Most cited references2

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          On -Adic Representations for Totally Real Fields

          A. Wiles (1986)
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            ON MODULAR CORRESPONDENCES FOR SP(N, Z) AND THEIR CONGRUENCE RELATIONS

            G. Shimura (1963)
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              Author and article information

              Journal
              17 January 1999
              Article
              math/9901156
              bd450b7a-4238-4d79-b6d7-3ab247cc3210
              History
              Custom metadata
              ANT-0164
              math.NT

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