Modularity Lifting for n-Dimensional Ordinary Galois Representations

JOINT IAS/PU NUMBER THEORY SEMINAR
Topic:Modularity Lifting for n-Dimensional Ordinary Galois Representations
Speaker:David Geraghty
Affiliation:Harvard University
Date:Friday, October 30
Time/Room:4:00pm - 5:00pm/Fine Hall -- 322

I will discuss a generalization of the modularity lifting theorems of Clozel, Harris and Taylor to the case of ordinary Galois representations. The result is obtained by applying the Taylor-Wiles method (with innovations due to Kisin and Taylor) over a Hida family. A key step is to construct an appropriate ordinary lifting ring and determine its irreducible components.