Mathematical Research Letters

Volume 23 (2016)

Number 5

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

Pages: 1469 – 1506



Xu Shen (Mathematisches Institut, Universität Bonn, Germany; and Fakultät für Mathematik, Universität Regensburg, Germany)


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.

Full Text (PDF format)

Published 12 January 2017