Explicit surjectivity of Galois representations attached to abelian surfaces and GL₂-varieties

2014/11/06 by Lombardo, Davide
#11F80 #11G10 #14K15 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1411.1703

Abstract

Let A be an absolutely simple abelian variety without (potential) complex multiplication, defined over the number field K. Suppose that either dim A=2 or A is of GL₂-type: we give an explicit bound ℓ₀(A,K) such that, for every prime ℓ>ℓ₀(A,K), the image of the absolute Galois group of K in Aut(T_ℓ(A)) is as large as it is allowed to be by endomorphisms and polarizations.

Related

• Galois representations attached to abelian varieties of CM type
• Abelian varieties over number fields, tame ramification and big Galois image
• Families of abelian varieties and large Galois images
• Explicit determination of the images of the Galois representations attached to abelian surfaces with End(A)=\Z
• Explicit open image theorems for abelian varieties with trivial endomorphism ring