1999/01/18 by Jacques Tilouine, Tilouine, Jacques, Eric Urban +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT
paper · pdf · doi:10.48550/arxiv.math/9901156
arxiv created 1999/01/18 · openalex publication_date 1999/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 underlinelambda 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_underlinelambda of Galois representations associated to underlinelambda. 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_underlinelambda 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".