Even Galois Representations and the Fontaine-Mazur Conjecture

Even Galois Representations and the Fontaine-Mazur Conjecture

-
Frank Calegari, Northwestern University
Fine Hall 214

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.