$p$-adic families of automorphic forms over some unitary Shimura varieties

TL;DR

This paper constructs eigenvarieties for overconvergent automorphic forms on certain unitary Shimura varieties and demonstrates the existence of Galois pseudo-characters via analytic continuation methods.

Contribution

It adapts existing methods to build eigenvarieties in higher dimensions and establishes Galois pseudo-characters over these spaces.

Findings

Construction of n-dimensional eigenvarieties for finite slope overconvergent eigenforms.

Existence of Galois pseudo-characters over the eigenvarieties.

Extension of analytic continuation techniques to these 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.