$p$-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 $(1,n-1)\times (0,n)\times \cdots \times (0,n)$ 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.

24 pages; revised version; minor changes; to appear in Math. Research Letters