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 p-adic Tate module of any non-CM elliptic curve over a given number field. In a collaboration with D. Ramakrishnan we provide first evidence in higher dimension. Namely, we establish a uniform irreducibility of Galois acting on the p-primary part of principally polarized Abelian 3-folds with multiplication by an imaginary quadratic field having no CM factors, under a technical condition which is void in the semi-stable case.