We prove, under mild hypotheses, that there are no irreducible twodimensional 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… (More)
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