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

### Luis Victor Dieulefait

Universitat de Barcelona, Spain

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## 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 ${\rm GL}_{2^m}(\mathbb{Q})$ 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 $f_i$.

## Cite this article

Luis Victor Dieulefait, Automorphy of $m$-fold tensor products of GL(2). Rev. Mat. Iberoam. 36 (2020), no. 2, pp. 407–434

DOI 10.4171/RMI/1134