Cohomology and Reciprocity

There are well known conjectures in the Langlands Programme which link regular motives to the
cohomology of arithmetic groups. The most successful approach to this problem so far comes out
of the work of Andrew Wiles. In this survey talk, I will discuss the extent to which these methods
can be generalized to situations where the underlying arithmetic group is $\mathrm{GL}_N(\mathbf{Z})$.