论文标题
安德森生成功能和德林菲尔德扭转扩展的泰勒系数
Taylor coefficients of Anderson generating functions and Drinfeld torsion extensions
论文作者
论文摘要
我们将我们的工作推广到Carlitz Prime Power Torsion扩展到任意等级的Drinfeld模块的扭转扩展。就像在卡里茨案例中一样，我们就安德森生成功能及其在统一根基上产生的功能的评估及其过度动力的评估来描述这些扩展。我们还提供了一个直接的证明，表明$ \ mathfrak {p} $ - ADIC TATE模块的图像位于$ \ Mathfrak {P} $ - 动机Galois Group的ADIC点。这是Chang和Papanikolas对$ T $ ADIC案件的相应结果的概括。
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.
