Hida theory over some unitary Shimura varieties without ordinary locus

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.

American Journal of Mathematics