Hida theory over some unitary Shimura varieties without ordinary locus

Riccardo Brasca (1) , Giovanni Rosso (2)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 Concordia University [Montreal]

We develop Hida theory for Shimura varieties of type A without ordinary locus. In particular we show that the dimension of the space of ordinary forms is bounded independently of the weight and that there is a module of Λ-adic cuspidal ordinary forms which is of finite type over Λ, where Λ is a twisted Iwasawa algebra.

Mots clés: Hida theory; p-adic modular forms; PEL-type Shimura varieties

Domaines: Théorie des nombres [math.NT]

Riccardo Brasca, Giovanni Rosso. Hida theory over some unitary Shimura varieties without ordinary locus. 2017. ⟨hal-01654535⟩