Abstract:
In 1969 Manin proved a uniform
version of Serre's celebrated result on the openness of the Galois
image in the automorphisms of the $\ell$-adic Tate module of any
non-CM elliptic curve over a given number field. Recently, in a
series of papers Cadoret and Tamagawa established a definitive
uniform open image result for the $\ell$-adic representations
attached to $1$-dimensional abelian families. In this lecture, based
on joint work with M. Dimitrov, we provide the first evidence in
higher dimension, for families of abelian 3-folds parametrized by
certain Picard modular surfaces.
Language: English
|
