  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.
