Number Theory Seminar

Half a century ago Manin proved a uniform version of Serre's celebrated result on the openness of the Galois image in the automorphisms of the l-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 result regarding the uniform boundedness of the l-primary torsion for 1-dimensional abelian families. In a collaboration with Dinakar Ramakrishnan we provide first evidence in higher dimension, in the case of abelian families parametrized by Picard modular surfaces over an imaginary quadratic field M. Namely, we establish a uniform irreducibility of Galois acting on the l-primary part of principally polarized Abelian 3-folds with multiplication by M, but without CM factors.