Number Theory Seminar
Patrick Allen
Northwestern
Modularity of nearly ordinary 2-adic residually dihedral Galois representations.
Abstract: Modularity lifting theorems are a tool for proving that p-adic
Galois representations come from modular (or automorphic) forms using the
assumption that its associated mod p representation comes from a modular
form. Due to their technical nature, the method encounters difficulties if
p divides the dimension of the representation, or when the mod p
representation has small image. We show how the 2-adic patching method of
Khare and Wintenberger combined with the strategy of Skinner and Wiles,
using Hida familes, can be used to prove modularity of some two
dimensional, 2-adic Galois representations over totally real fields that
are nearly ordinary and residually dihedral. As an application we deduce
modularity of some elliptic curves over totally real fields that have good
ordinary or multiplicative reduction at places above 2.
Tuesday November 12, 2013 at 1:00 PM in SEO 636