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arXiv · 2008.07136

Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions

Andreas Maurischat·Rudolph Perkins
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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 $\mathfrak{p}$-adic Tate module lies in the $\mathfrak{p}$-adic points of the motivic Galois group. This is a generalization of the corresponding result of Chang and Papanikolas for the $t$-adic case.

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Andreas Maurischat, Rudolph Perkins. 2020-08-17. Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions. https://doi.org/10.1142/s1793042122500099

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