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Papers by Nuria Vila
Mathematische Zeitschrift, 2007
We study compatible families of four-dimensional Galois representations constructed in theétale c... more We study compatible families of four-dimensional Galois representations constructed in theétale cohomology of a smooth projective variety. We prove a theorem asserting that the images will be generically large if certain conditions are satisfied. We only consider representations with coefficients in an imaginary quadratic field. We apply our result to an example constructed by Jasper Scholten (see [Sc]), obtaining a family of linear groups and one of unitary groups as Galois groups over Q.
American Journal of Mathematics, 2004
We study compatible families of three-dimensional Galois representations constructed in the tale ... more We study compatible families of three-dimensional Galois representations constructed in the tale cohomology of a smooth projective variety. We prove a theorem asserting that the images will be generically large if certain easy to check conditions are satisfied. We only consider representations with coefficients in an imaginary quadratic field. For primes inert in this field, the residual representations (when irreducible) are unitary. We apply our result to an example constructed by van Geemen and Top (see [vG-T1]), obtaining a family of special linear groups and one of special unitary groups as Galois groups over Q. We also consider the case of a cohomological modular form for a congruence subgroup of SL(3, Z). Assuming Clozel's conjecture stating that a geometric family of three-dimensional Galois representations can be attached to it, we give conditions on the modular form guaranteeing the validity of the result on the largeness of the images. We apply this result to several examples.
Mathematische Zeitschrift, 2007
We study compatible families of four-dimensional Galois representations constructed in theétale c... more We study compatible families of four-dimensional Galois representations constructed in theétale cohomology of a smooth projective variety. We prove a theorem asserting that the images will be generically large if certain conditions are satisfied. We only consider representations with coefficients in an imaginary quadratic field. We apply our result to an example constructed by Jasper Scholten (see [Sc]), obtaining a family of linear groups and one of unitary groups as Galois groups over Q.
American Journal of Mathematics, 2004
We study compatible families of three-dimensional Galois representations constructed in the tale ... more We study compatible families of three-dimensional Galois representations constructed in the tale cohomology of a smooth projective variety. We prove a theorem asserting that the images will be generically large if certain easy to check conditions are satisfied. We only consider representations with coefficients in an imaginary quadratic field. For primes inert in this field, the residual representations (when irreducible) are unitary. We apply our result to an example constructed by van Geemen and Top (see [vG-T1]), obtaining a family of special linear groups and one of special unitary groups as Galois groups over Q. We also consider the case of a cohomological modular form for a congruence subgroup of SL(3, Z). Assuming Clozel's conjecture stating that a geometric family of three-dimensional Galois representations can be attached to it, we give conditions on the modular form guaranteeing the validity of the result on the largeness of the images. We apply this result to several examples.