Let be a Drinfeld -module of characteristic over a finitely generated field . Previous articles determined the image of the absolute Galois group of up to commensurability in its action on all prime-to- torsion points of , or equivalently, on the prime-to- adelic Tate module of . In this article we consider in addition a finitely generated torsion free -submodule of for the action of through . We determine the image of the absolute Galois group of up to commensurability in its action on the prime-to- division hull of , or equivalently, on the extended prime-to- adelic Tate module associated to and .
"Kummer theory for Drinfeld modules." Algebra Number Theory 10 (2) 215 - 234, 2016. https://doi.org/10.2140/ant.2016.10.215