Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions
arXiv:2008.07136 · doi:10.1142/S1793042122500099
Abstract
We generalize our work on Carlitz prime power torsion extension to torsion extensions of Drinfeld modules of arbitrary rank. As in the Carlitz case, we give a description of these extensions in terms of evaluations of Anderson generating functions and their hyperderivatives at roots of unity. We also give a direct proof that the image of the Galois representation attached to the -adic Tate module lies in the -adic points of the motivic Galois group. This is a generalization of the corresponding result of Chang and Papanikolas for the -adic case.
16 pages; v1->v2: Changes in Section 5: Corrected some flaws and expanded the explanations