Revista Matemática Iberoamericana

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Published online first: 2020-01-10
DOI: 10.4171/rmi/1134

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

Luis Victor Dieulefait[1]

(1) Universitat de Barcelona, Spain

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 $f_i$.

Keywords: Automorphic forms, Galois representations, Langlands program

Dieulefait Luis Victor: Automorphy of $m$-fold tensor products of GL(2). Rev. Mat. Iberoam. Electronically published on January 10, 2020. doi: 10.4171/rmi/1134 (to appear in print)