Non-openness of v-adic Galois representation for A-motives
Number Theory
2019-11-11 v2
Abstract
Drinfeld-modules and -motives are the function field analogous of elliptic curves and abelian varieties. For the latter one can construct the -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 -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.
Cite
@article{arxiv.1910.03037,
title = {Non-openness of v-adic Galois representation for A-motives},
author = {Maike Ella Elisabeth Frantzen},
journal= {arXiv preprint arXiv:1910.03037},
year = {2019}
}
Comments
v1: 14 pages, v2: 15 pages