Automorphy of $m$-fold tensor products of GL(2)

Abstract

We prove that for any $m>1$, given any $m$-tuple of Hecke eigenforms $f_i$ of level $1$ whose weights satisfy the usual regularity condition, there is a self-dual cuspidal automorphic form $\pi$ of ${\mathrm{GL}}_{2^m}(\mathbb{Q})$ corresponding to their tensor product, i.e., such that the system of Galois representations attached to $\pi$ agrees with the tensor product of the ones attached to the cuspforms $f_i$.