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 $𝔭$-adic Tate module lies in the $𝔭$-adic points of the motivic Galois group. This is a generalization of the corresponding result of Chang and Papanikolas for the $t$-adic case.

中文翻译：

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Anderson 生成函数和 Drinfeld 扭转扩展的泰勒系数

我们将我们在 Carlitz 素幂扭转扩展上的工作推广到任意秩的 Drinfeld 模块的扭转扩展上。与 Carlitz 案例一样，我们根据对 Anderson 生成函数及其统一根上的超导数的评估来描述这些扩展。我们还直接证明了伽罗瓦表示的图像附加到$𝔭$-adic Tate 模块位于 $𝔭$- 动机伽罗瓦群的进取点。这是 Chang 和 Papanikolas 对$吨$-adic案例。