-adic families of automorphic forms over some unitary Shimura varieties

Abstract

We construct some n-dimensional eigenvarieties for finite slope overconvergent eigenforms over some unitary Shimura varieties with signature (1, n - 1) x (0, n) x ... x (0, n) by adapting Andreatta-Iovita-Pilloni's method. We also show that there are some Galois pseudo-characters over our eigenvarieties by studying analytic continuation of finite slope eigenforms over these Shimura varieties.