论文标题
功能字段算术中的调节器
Regulators in the Arithmetic of Function Fields
论文作者
论文摘要
作为在[GAZ]发起的$ a-Motivic共同体研究的自然续集，我们为严格的分析性琐碎的Anderson $ a $ to-Motives开发了一个监管机构的概念。根据猜想的数字图像，我们将其定义为由hodge-pink实现函数的精确性引起的延伸模块级别的形态。本文的目的是双重的：我们首先证明了$ a-Motivic的共同体的有限结果，并且在权重假设下，我们然后证明监管机构的来源和目标具有相同的维度。令作者感到惊讶的是，该监管机构的形象可能没有完全排名，从而阻止了贝林森著名猜想的类似物在我们的环境中保持。
As a natural sequel for the study of $A$-motivic cohomology, initiated in [Gaz], we develop a notion of regulator for rigid analytically trivial Anderson $A$-motives. In accordance with the conjectural number field picture, we define it as the morphism at the level of extension modules induced by the exactness of the Hodge-Pink realization functor. The purpose of this text is twofold: we first prove a finiteness result for $A$-motivic cohomology and, under a weight assumption, we then show that the source and the target of regulators have the same dimension. It came as a surprise to the author that the image of this regulator might not have full rank, preventing the analogue of a renowned conjecture of Beilinson to hold in our setting.
