English

Even Galois Representations and the Fontaine--Mazur conjecture II

Number Theory 2015-05-20 v2

Abstract

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q)\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.

Keywords

Cite

@article{arxiv.1012.4819,
  title  = {Even Galois Representations and the Fontaine--Mazur conjecture II},
  author = {Frank Calegari},
  journal= {arXiv preprint arXiv:1012.4819},
  year   = {2015}
}

Comments

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