发表机构
RWTH Aachen University; Fairfield University（亚琛工业大学; 费尔菲尔德大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在伽罗瓦表示假设下，将Drinfeld模周期超越性结果推广至一般Anderson $t$-模，并应用于有限多个Drinfeld模的周期与准周期代数关系，支持Mumford-Tate猜想。
AI 中文摘要
Anderson模的周期、准周期及其超导数的超越性问题在函数域上的数论中具有重要研究意义。在Drinfeld模的情形下，该问题已由第二作者解决。本文证明，在对其伽罗瓦表示满足一定假设的条件下，这些结果对一般的Anderson $t$-模也成立。证明利用了第一作者通过相关$t$-模的刚性解析平凡化对$\frak{p}$-adic伽罗瓦表示的显式描述，以及$t$-模和$t$-模的延拓。该一般结果被应用于确定有限多个Drinfeld模的周期、准周期及其超导数之间的代数关系。此外，我们的结果为Anderson模的Mumford-Tate猜想提供了更多证据。
英文摘要
Transcendence questions of periods and quasi-periods of Anderson modules, as well as the hyperderivatives thereof, are of major interest in number theory over function fields. In the case of Drinfeld modules, this question was answered by the second author. In this paper, we show that these results hold for general Anderson $t$-modules under certain assumptions on their Galois representations. The proofs use the explicit description of the $\mathfrak{p}$-adic Galois representation of the first author by means of a rigid analytic trivialization of the associated $t$-motive, as well as prolongations of $t$-modules and $t$-motives. The general result is applied to determine algebraic relations between periods and quasi-periods, and their hyperderivatives, of finitely many Drinfeld modules. Along the way, our results provide more evidence for the Mumford-Tate conjecture for Anderson modules.
Comments28 pages
