M中的伽罗瓦群的计算帕帕尼克拉斯对卡利兹对数的研究
Computation of the Galois groups occuring in M. Papanikolas's study of Carlitz logarithms
摘要：
本文给出了一个关于定义在正特征域上的Tannakian范畴的对象$U$的伽罗瓦群的幂幺根的计算定理，该对象是单位对象的半单扩张.然后，我们给出了一个标准的代数解的对象的线性相关的扩展组。我们将这些结果应用于M. Papanikolas;特别是，我们给出了另一种证明的代数独立的Carlitz矩阵。
英文摘要：
In this note, we state a theorem of compution of the unipotent radical of the Galois group of an object $U$ of a tannakian category defined over a field of positive characteristic, extension of the unit object by a semi-simple one. We then give a criteria of algebricity of solutions of the objects in terms of linear dependences in groups of extension. We apply these results to the tanakian framework of $t$-motives developped by M. Papanikolas; in particular, we give an alternative proof of the algebraic independence of Carlitz logarithms.
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