Even Galois representations and the Fontaine-Mazur conjecture

摘要

We prove, under mild hypotheses, that there are no irreducible two-dimensional ordinary even Galois representations of Gal(Q?/Q) with distinct Hodge-Tate weights. This is in accordance with the Fontaine-Mazur conjecture. If K/Q is an imaginary quadratic field, we also prove (again, under certain hypotheses) that Gal(Q?/K) does not admit irreducible two-dimensional ordinary Galois representations of non-parallel weight.