Abstract
For an elliptic curve without potential complex multiplication we bound the index of the image of Gal in GL, the representation being given by the action on the Tate modules of at the various primes. The bound is explicit and only depends on and on the stable Faltings height of . We also prove a result relating the structure of closed subgroups of GL to certain Lie algebras naturally attached to them.
Citation
Davide Lombardo. "Bounds for Serre's open image theorem for elliptic curves over number fields." Algebra Number Theory 9 (10) 2347 - 2395, 2015. https://doi.org/10.2140/ant.2015.9.2347
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