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Modularity lifting theorems for Galois representations of unitary type

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

Published online by Cambridge University Press:  18 March 2011

Lucio Guerberoff
Lucio Guerberoff*
Affiliation:
Departamento de Matemática, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria C.P.: 1428, Buenos Aires, Argentina
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Abstract

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We prove modularity lifting theorems for ℓ-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine–Laffaille condition at ℓ. This extends the results of Clozel, Harris and Taylor, and the subsequent work by Taylor. The proof uses the Taylor–Wiles method, as improved by Diamond, Fujiwara, Kisin and Taylor, applied to Hecke algebras of unitary groups, and results of Labesse on stable base change and descent from unitary groups to GLn.

Keywords

modularityGalois representationsunitary groups

MSC classification

Secondary: 11F80: Galois representations 11R39: Langlands-Weil conjectures, nonabelian class field theory 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 4 , July 2011 , pp. 1022 - 1058
Copyright
Copyright © Foundation Compositio Mathematica 2011

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