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 Gal (K̅/K) in Aut (Tℓ (A)) is as large as it is allowed to be by endomorphisms and polarizations.
Explicit surjectivity of Galois representations for abelian surfaces and GL(2)-varieties
LOMBARDO, DAVIDE
2016-01-01
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 Gal (K̅/K) in Aut (Tℓ (A)) is as large as it is allowed to be by endomorphisms and polarizations.File in questo prodotto:
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