10/1/2009
Frank Calegari
Northwestern University
Even Galois Representations and the Fontaine-Mazur Conjecture
We prove, under mild hypotheses, there are no irreducible two-dimensional ordinary even Galois representations of the Galois group of Q with distinct Hodge-Tate weights, in accordance with the Fontaine-Mazur conjecture. We also show how this method can be applied to a related circle of problems.