Modularity lifting theorems for Galois representations of unitary type

Details Modularity lifting theorems for Galois representations of unitary type Modularity lifting theorems for Galois representations of unitary type

2009-06-23

arxiv.org/abs/0906.4189v3

Mathematics

Number Theory

32 pages, final version incorporating referee's suggestions

Scientific paper

We prove modularity lifting theorems for l-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type 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 GL_n.

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