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1 February 2017 Level-raising and symmetric power functoriality, III
Laurent Clozel, Jack A. Thorne
Duke Math. J. 166(2): 325-402 (1 February 2017). DOI: 10.1215/00127094-3714971

Abstract

The simplest case of the Langlands functoriality principle asserts the existence of the symmetric powers Symn of a cuspidal representation of GL(2) over the adèles of F, where F is a number field. In 1978, Gelbart and Jacquet proved the existence of Sym2. After this, progress was slow, eventually leading, through the work of Kim and Shahidi, to the existence of Sym3 and Sym4. In this series of articles we revisit this problem using recent progress in the deformation theory of modular Galois representations. As a consequence, our methods apply only to classical modular forms on a totally real number field; the present article proves the existence, in this “classical” case, of Sym6 and Sym8.

Citation

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Laurent Clozel. Jack A. Thorne. "Level-raising and symmetric power functoriality, III." Duke Math. J. 166 (2) 325 - 402, 1 February 2017. https://doi.org/10.1215/00127094-3714971

Information

Received: 17 July 2014; Revised: 10 December 2015; Published: 1 February 2017
First available in Project Euclid: 9 December 2016

zbMATH: 1339.11060
MathSciNet: MR3600753
Digital Object Identifier: 10.1215/00127094-3714971

Subjects:
Primary: 11F03 , 11F66
Secondary: 11F80

Keywords: Galois representations , Hilbert modular forms , Langlands functoriality

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 2 • 1 February 2017
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