# Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture

@inproceedings{Dieulefait2003ExistenceOF,
title={Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture},
author={L. Dieulefait},
year={2003}
}
Abstract 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({a2 p}) = ℚ always comes from an abelian variety. We… Expand
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