Geodesic
Automorphic realization of residual Galois representations
Journal of the European Mathematical Society, Tome 12 (2010) no. 4, pp. 915-937.

Voir la notice de l'article provenant de la source EMS Press

We show that it is possible in rather general situations to obtain a finite-dimensional modular representation ρ of the Galois group of a number field F as a constituent of one of the modular Galois representations attached to automorphic representations of a general linear group over F, provided one works “potentially.” The proof is based on a close study of the monodromy of the Dwork family of Calabi–Yau hypersurfaces; this in turn makes use of properties of rigid local systems and the classification of irreducible subgroups of finite classical groups with certain sorts of generators.
DOI : 10.4171/jems/219
Classification : 11-XX, 20-XX, 34-XX, 00-XX
Keywords: Galois representations, automorphy, hypergeometric local systems 
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     author = {Robert M. Guralnick and Michael Harris and Nicholas M. Katz},
     title = {Automorphic realization of residual {Galois} representations},
     journal = {Journal of the European Mathematical Society},
     pages = {915--937},
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     year = {2010},
     doi = {10.4171/jems/219},
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Robert M. Guralnick; Michael Harris; Nicholas M. Katz. Automorphic realization of residual Galois representations. Journal of the European Mathematical Society, Tome 12 (2010) no. 4, pp. 915-937. doi : 10.4171/jems/219. http://geodesic.mathdoc.fr/articles/10.4171/jems/219/

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