Geodesic
Lifting Galois representations and a conjecture of Fontaine and Mazur
Documenta mathematica, Tome 6 (2001), pp. 419-445
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Mumford has constructed 4-dimensional abelian varieties with trivial endomorphism ring, but whose Mumford–Tate group is much smaller than the full symplectic group. We consider such an abelian variety, defined over a number field F, and study the associated p-adic Galois representation. For F sufficiently large, this representation can be lifted to Gm​(Qp​)×SL2​(Qp​)3. Such liftings can be used to construct Galois representations which are geometric in the sense of a conjecture of Fontaine and Mazur. The conjecture in question predicts that these representations should come from algebraic geometry. We confirm the conjecture for the representations constructed here.
DOI : 10.4171/dm/109
Classification : 11F80, 11G10, 14K15
Mots-clés : motives, geometric Galois representation, fontaine--Mazur conjecture 
@article{10_4171_dm_109,
     author = {Rutger Noot},
     title = {Lifting {Galois} representations and a conjecture of {Fontaine} and {Mazur}},
     journal = {Documenta mathematica},
     pages = {419--445},
     year = {2001},
     volume = {6},
     doi = {10.4171/dm/109},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/109/}
}
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Rutger Noot. Lifting Galois representations and a conjecture of Fontaine and Mazur. Documenta mathematica, Tome 6 (2001), pp. 419-445. doi: 10.4171/dm/109

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