Abstract
Drinfeld modules and A-motives s are the function field analogs of elliptic curves and abelian varieties. For both Drinfeld modules and [Formula: see text]-motives, one can construct their [Formula: see text]-adic Galois representations and ask whether the images are open. For Drinfeld modules, this question has been answered by Richard Pink and his co-authors; however, this question has not been addressed for [Formula: see text]-motives. Here, we clarify the rank-one case for A-motives and show that the image of Galois is open if and only if the virtual dimension is prime to the characteristic of the ground field.
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