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arXiv · 1012.4819

Even Galois Representations and the Fontaine--Mazur conjecture II

Frank Calegari
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Abstract

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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Frank Calegari. 2011-09-29. Even Galois Representations and the Fontaine--Mazur conjecture II. https://doi.org/10.1007/s00222-010-0297-0

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