Even Galois Representations and the Fontaine--Mazur conjecture II

Details Even Galois Representations and the Fontaine--Mazur conjecture II Even Galois Representations and the Fontaine--Mazur conjecture II

2010-12-21

arxiv.org/abs/1012.4819v2

Mathematics

Number Theory

Updated to take into account suggestions of the referee; the main theorems remain unchanged

Scientific paper

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of $\Gal(\Qbar/\Q)$ which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the author. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric (= de Rham) deformations.

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