A pr 2 00 3 Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture

@inproceedings{Dieulefait2003AP2,
  title={A pr 2 00 3 Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture},
  author={Luis V. Dieulefait},
  year={2003}
}
In a previous article, we have proved a result asserting the existence of a compatible family of Galois representations containing a given crystalline irreducible odd two-dimensional representation. We apply this result to establish new cases of the Fontaine-Mazur conjecture, namely, an irreducible Barsotti-Tate λ-adic 2-dimensional Galois representation unramified at 3 and such that the traces ap of the images of Frobenii verify Q({a2p}) = Q always comes from an abelian variety. We also show… CONTINUE READING

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