Abstract

The aim of this thesis is to present the paper of Kottwitz with the same title. The first 4 chapters are a rapid review of the prerequisites and the main result of the paper is presented in chapter 5 and some ideas of the proof are given in chapter 6. The objective of the paper is to construct Galois representations associated to cohomological automorphic representations i.e. automorphic representations occurring in the cohomology of a certain Shimura variety. The difficult part lies in proving that this association matches up the local Satake parameter of the automorphic representations with the local Frobenius conjugacy class of the Galois representation at places of good reduction. We try to present the material with as much detail as possible, except at some places we either restrict ourselves to providing references for further details or work instead with the case of GL2, where the associated Shimura varieties (modular curves) have a much simpler moduli interpretation.