On the classification of geometric families of 4-dimensional Galois representations

Details On the classification of geometric families of 4-dimensional Galois representations On the classification of geometric families of 4-dimensional Galois representations

2008-10-13

arxiv.org/abs/0810.2203v2

Mathematics

Number Theory

A few details added in the proof of the main result

Scientific paper

We give a classification theorem for certain four-dimensional families of geometric $\lambda$-adic Galois representations attached to a pure motive. More precisely, we consider families attached to the cohomology of a smooth projective variety defined over $\Q$ with coefficients in a quadratic imaginary field, non-selfdual and with four different Hodge-Tate weights. We prove that the image is as large as possible for almost every $\lambda$ provided that the family is irreducible and not induced from a family of smaller dimension. If we restrict to semistable families an even simpler classification is given. A version of the main result is given for the case where the family is attached to an automorphic form.

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