Prolongations of $t$-Motives and Algebraic Independence of Periods
Prolongations of $t$-Motives and Algebraic Independence of Periods
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$t$-动机的延长和周期的代数独立性
DOI：
10.4171/dm/635
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发表时间：
2017
影响因子：
0.9
通讯作者：
A. Maurischat
中科院分区：
文献类型：
--
作者：
A. Maurischat
在这篇文章中，我们证明了周期格生成元的$n$次张量幂的Carlitz模的坐标是代数独立的，如果$n$是素的特征。然而，该文件的主要部分，是致力于一般建设的$T$-动机，我们称之为延长，并提供了必要的背景，我们证明了代数的独立性。另一个怀疑是一个定理，它表明了安德森-塔库尔函数$\omega（t）$的超超越性，即$\omega（t）$和它关于$t$的所有超导数都是代数独立的。
In this article we show that the coordinates of a period lattice generator of the $n$-th tensor power of the Carlitz module are algebraically independent, if $n$ is prime to the characteristic. The main part of the paper, however, is devoted to a general construction for $t$-motives which we call prolongation, and which gives the necessary background for our proof of the algebraic independence. Another incredient is a theorem which shows hypertranscendence for the Anderson-Thakur function $\omega(t)$, i.e. that $\omega(t)$ and all its hyperderivatives with respect to $t$ are algebraically independent.