p-adic Asai transfer

Abstract

Let K/Q be a real quadratic field. Given an automorphic representation pi for GL(2)/K, let As-+/-(pi) denote the plus/minus Asai transfer of pi to an automorphic representation for GL(4)/Q. In this paper, we construct a rigid analytic map from a subvariety of the universal eigenvariety of GL(2)/K to an eigenvariety of GL(4)/Q, which at nice classical points interpolate this Asai transfer.