P-Adic Asai Transfer

Abstract

Let K /Q be a real quadratic field. Given an automorphic representation 1t for GL2/ K, let As±(1r) denote the plus/minus Asai transfer of 1t to an automorphic representation for GL4/Q. In this paper, we construct a rigid analytic map from a subvariety of the universal eigenvariety of GLi/ K to an eigenvariety of G~/Q, which at nice classical points interpolate this Asai transfer.