Rigidity of automorphic Galois representations over CM fields

Thesis

We show the vanishing of adjoint Bloch-Kato Selmer groups of automorphic Galois representations over CM fields. This proves their rigidity in the sense that they have no deformations which are de Rham. In order for this to make sense we also prove that automorphic Galois representations over CM fields are de Rham themselves. Our methods draw heavily from the ten author paper, where these Galois representations were studied extensively. Another crucial piece of inspiration comes from the work of P. Allen who used the smoothness of certain local deformation rings in characteristic zero to obtain rigidity in the polarized case.

Authors: A'Campo, L

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Subjects: Number theory