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

Citation
J. Tilouine et E. Urban, Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations, ANN SCI EC, 32(4), 1999, pp. 499-574
Citations number
49
Categorie Soggetti
Mathematics
Journal title
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE
ISSN journal
00129593 → ACNP
Volume
32
Issue
4
Year of publication
1999
Pages
499 - 574
Database
ISI
SICI code
0012-9593(199907/08)32:4<499:SPFOSC>2.0.ZU;2-3
Abstract
Let F be a totally real field and G = GSp(4)(/F). In this paper, we show un der 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 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. Lf F = Q, the number of variables is three. Moreover, in this case, we construct the three-variable p-adic family p lam bda of Galois representations associated to lambda. Finally, under geometri c assumptions (which would be satisfied if one proved that the Galois repre sentations in the family come from Grothmdieck motives), we show that p lam bda is nearly ordinary for the dual parabolic of P. (C) Elsevier, Paris.