Potential Automorphy for Compatible Systems of l-Adic Galois Representations

Potential Automorphy for Compatible Systems of l-Adic Galois Representations - David Geraghty

David Geraghty
Princeton University; Member, School of Mathematics
November 18, 2010

I will describe a joint work with Barnet-Lamb, Gee and Taylor where we establish a potential automorphy result for compatible systems of Galois representations over totally real and CM fields. This is deduced from a potential automorphy result for single l-adic Galois representations satisfying a `diagonalizability' condition at the places dividing l.