Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture
نویسنده
چکیده
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 the non-existence of irreducible Barsotti-Tate 2-dimensional Galois representations of conductor 1 and apply this to the irreducibility of Galois representations on level 1 genus 2 Siegel cusp forms. 1 Existence of families The following is a slight generalization of a result proved in [D3], which follows from the results and techniques in [T1], [T2]: ∗e-mail: [email protected]. Supported by MECD postdoctoral fellowship at the Centre de Recerca Matemática from the Ministerio de Educación y Cultura
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