p-adic Asai transfer

Abstract

Let $K/Q$ be a real quadratic field. Given an automorphic representation $\pi$ for $G{L}_2/K$, let $A{s}^{\pm }(\pi )$ denote the plus/minus Asai transfer of $\pi$ to an automorphic representation for $G{L}_4/Q$. In this paper, we construct a rigid analytic map from the universal eigenvariety of $G{L}_2/K$ to the universal eigenvariety of $G{L}_4/Q$, which at nice classical points interpolate this Asai transfer.

18 pages