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

We construct some $n$-dimensional eigenvarieties for finite slope overconvergent eigenforms over some unitary Shimura varieties with signature $(1, n - 1) \times (0, n) \times \dotsm \times (0, n)$ 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.

2010 Mathematics Subject Classification

Primary 11F85, 11G18. Secondary 14G35.

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Accepted 9 June 2015

Published 12 January 2017