Even Galois Representations and the Fontaine--Mazur conjecture II

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.

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

References in corpus (3)

• Local-global compatibility and the action of monodromy on nearby cycles
• Even Galois Representations and the Fontaine--Mazur conjecture II
• A Cuspidality Criterion for the Exterior Square Transfer of Cusp Forms on GL(4)

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• Irreducibility of geometric Galois representations and the Tate conjecture for a family of elliptic surfaces