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arXiv · 1910.03037

Non-openness of v-adic Galois representation for A-motives

Maike Ella Elisabeth Frantzen
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Abstract

Drinfeld-modules and $A$-motives are the function field analogous of elliptic curves and abelian varieties. For the latter one can construct the $l$-adic Galois representation and can ask if its image is open. For Drinfeld-modules this question was answered by Pink and his coauthors. 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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Maike Ella Elisabeth Frantzen. 2019-10-07. Non-openness of v-adic Galois representation for A-motives. https://arxiv.org/abs/1910.03037

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