On uniform large Galois images for modular abelian varieties

Eknath Ghate (1) , Pierre Parent (2)

1 School of Mathematics [TIFR]
2 IMB - Institut de Mathématiques de Bordeaux

We formulate a question regarding uniform versions of "large Galois image properties" for modular abelian varieties of higher dimension, generalizing the well-known case of elliptic curves. We then answer our question affirmatively in the exceptional image case, and provide lower estimates for uniform bounds in the remaining cases.

Mots clés: Galois representations; modular forms; abelian varieties

Domaines: Théorie des nombres [math.NT]

Eknath Ghate, Pierre Parent. On uniform large Galois images for modular abelian varieties. Bull. London Math. Soc., 2012, 44, pp.1169-1181. ⟨10.1112/blms/bds041⟩. ⟨hal-00772175⟩