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 $\mathrm{\Lambda }$-adic cuspidal ordinary forms which is of finite type over $\mathrm{\Lambda }$, where $\mathrm{\Lambda }$ is a twisted Iwasawa algebra.