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 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