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Galois representations attached to automorphic forms on ${\rm GL}_2$ over ${\rm CM}$ fields

Part of: Lie groups Algebraic number theory: global fields Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  26 March 2014

Chung Pang Mok
Chung Pang Mok*
Affiliation:
Hamilton Hall, McMaster University, Hamilton, Ontario, L8S 4K1, Canada email cpmok@math.mcmaster.ca
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Abstract

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In this paper we generalize the work of Harris–Soudry–Taylor and construct the compatible systems of two-dimensional Galois representations attached to cuspidal automorphic representations of cohomological type on ${\rm GL}_2$ over a CM field with a suitable condition on their central characters. We also prove a local-global compatibility statement, up to semi-simplification.

Keywords

automorphic representationsGalois representations

MSC classification

Secondary: 11R39: Langlands-Weil conjectures, nonabelian class field theory 11F80: Galois representations 22E55: Representations of Lie and linear algebraic groups over global fields and adèle rings
Type
Research Article
Information
Compositio Mathematica , Volume 150 , Issue 4 , April 2014 , pp. 523 - 567
Copyright
© The Author 2014 

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