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

Luis V. Dieulefait

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

Number Theory 2014-01-21 v2

Authors: Luis V. Dieulefait

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 $\GL_{2^m}(\Q)$ 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

automorphy tensor product GL(2) Hecke eigenforms Galois representations cuspidal automorphic form

Cite

@article{arxiv.1212.4423,
  title  = {Automorphy of m-fold tensor products of GL(2)},
  author = {Luis V. Dieulefait},
  journal= {arXiv preprint arXiv:1212.4423},
  year   = {2014}
}

Comments

some details (concerning ordinary representations) added to the proof of Theorem 2.1

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