Potential Automorphy for Compatible Systems of l-Adic Galois Representations

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Topic:Potential Automorphy for Compatible Systems of l-Adic Galois Representations
Speaker:David Geraghty
Affiliation:Princeton University; Member, School of Mathematics
Date:Thursday, November 18
Time/Room:2:15pm - 3:15pm/S-101

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.