Serre–Tate theory for moduli spaces of PEL type
Several-variable -adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
Shimura varieties with -level via Hecke algebra isomorphisms: the Drinfeld case
We study the local factor at of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the Langlands-Kottwitz counting method. We explicitly determine the corresponding test functions in suitable Hecke algebras, and show their centrality by determining their images under the Hecke algebra isomorphisms of Goldstein, Morris, and Roche.
Siegel varieties and -adic Siegel modular forms.
Some remarks on almost rational torsion points
For a commutative algebraic group over a perfect field , Ribet defined the set of almost rational torsion points of over . For positive integers , we show there is an integer such that for all tori of dimension at most over number fields of degree at most , . We show the corresponding result for abelian varieties with complex multiplication, and under an additional hypothesis, for elliptic curves without complex multiplication. Finally, we show that except for an explicit finite...
Stark–Heegner points on modular jacobians
Sur la constante de Hida des courbes modulaires et des courbes de Shimura
La correspondance de Shimizu et Jacquet-Langlands donne des relations entre les quotients de la partie nouvelle de la jacobienne de et ceux de la partie nouvelle de la jacobienne de certaines courbes de Shimura associées. Nous comparons dans ce texte les congruences entre formes modulaires pour des quotients qui sont associés dans cette correspondance.
Sur la mauvaise réduction des courbes de Shimura
Sur la théorie de Hida pour le groupe
Nous construisons des familles ordinaires -adiques de formes modulaires pour le groupe . Notre travail généralise et précise des travaux antérieurs de Hida.
Sur une formule de Shioda et Mitani
Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere
We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system....