Geometric families of 4-dimensional Galois representations with generically large images

Details Geometric families of 4-dimensional Galois representations with generically large images Geometric families of 4-dimensional Galois representations with generically large images

2004-09-17

arxiv.org/abs/math/0409300v1

Mathematics

Number Theory

Scientific paper

We study compatible families of four-dimensional Galois representations constructed in the \'{e}tale 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, obtaining a family of linear groups and one of unitary groups as Galois groups over $\mathbb{Q}$.

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