On uniform large Galois images for modular abelian varieties

Eknath Ghate, Pierre Parent

Published 2011-09-29Version 1

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.