Even Galois Representations and the Fontaine-Mazur conjecture

JOINT IAS/PU NUMBER THEORY SEMINAR
Topic:Even Galois Representations and the Fontaine-Mazur conjecture
Speaker:Frank Calegari
Affiliation:Northwestern University; Member, School of Mathematics
Date:Thursday, October 14
Time/Room:4:30pm - 5:30pm/S-101

Fontaine and Mazur have a remarkable conjecture that predicts which (p-adic) Galois representations arise from geometry. In the special case of two dimensional representations with distinct Hodge-Tate weights, they further conjecture that these "geometric" representations are also modular. Kisin has proven this conjecture in almost all cases under the assumption that the action of complex conjugation has determinant -1. We remove this restriction. In the case of even Galois representations, this generalizes previous work in which the representation was assumed to be ordinary.