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

2014/05/29 by Xu Shen, Shen, Xu
Mathematics · #11F85 #14G35 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F85 #msc:14G35

paper · pdf · doi:10.48550/arxiv.1405.7587

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

arxiv created 2015/06/11 · arxiv updated 2015/06/12

Abstract

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

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