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On the potential automorphy of certain odd-dimensional Galois representations

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

Published online by Cambridge University Press:  10 March 2010

Thomas Barnet-Lamb
Thomas Barnet-Lamb*
Affiliation:
Department of Mathematics, Harvard University, Cambridge, MA 02138, USA (email: tbl@math.harvard.edu)
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Abstract

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In a previous paper, the potential automorphy of certain Galois representations to GLn for n even was established, following the work of Harris, Shepherd–Barron and Taylor and using the lifting theorems of Clozel, Harris and Taylor. In this paper, we extend those results to n=3 and n=5, and conditionally to all other odd n. The key additional tools necessary are results which give the automorphy or potential automorphy of symmetric powers of elliptic curves, most notably those of Gelbert, Jacquet, Kim, Shahidi and Harris.

Keywords

Galois representationpotential automorphypotential modularityDwork hypersurface

MSC classification

Secondary: 11R39: Langlands-Weil conjectures, nonabelian class field theory 11F23: Relations with algebraic geometry and topology

Information

Type
Research Article
Information
Compositio Mathematica , Volume 146 , Issue 3 , May 2010 , pp. 607 - 620
Copyright
Copyright © Foundation Compositio Mathematica 2010

References

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