论文标题
Carlitz Twist：他们的动机共同体，调节器，Zeta值和多组载体
Carlitz twists: their motivic cohomology, regulators, zeta values and polylogarithms
论文作者
论文摘要
[gaz22b]中的第一作者介绍了整体$ t $ - 动感的共同体和（刚性分析性的）安德森（Anderson）$ t $ - 动力的类模块。本文在Carlitz $ t $ -motive的特定情况下，致力于他们的决心，即功能字段$ \ usepline $ \ usepline {a} $ tate twist twists $ \ mathbb {z z}（n）$。我们发现这些模块与功能场算术的基本对象有关：整体$ t $ - 动力共同体控制carlitz polylogarithms之间的线性关系，其扭力以Bernoulli-Carlitz数字和班级模块的拟合理想为ZETA的拟合人数。我们还表达了$ \ upessuess {a}（n）$的调节剂，以$ n $ $ n $在广义的carlitz polygariths方面；在使用Anderson-Brownawell-Papanikolas标准建立了差异理论的代数关系之后，我们证明监管机是同构的，并且只有当$ n $对特征是主要的。
The integral $t$-motivic cohomology and the class module of a (rigid analytically trivial) Anderson $t$-motive were introduced by the first author in [Gaz22b]. This paper is devoted to their determination in the particular case of tensor powers of the Carlitz $t$-motive, namely, the function field counterpart $\underline{A}(n)$ of Tate twists $\mathbb{Z}(n)$. We find out that these modules are in relation with fundamental objects of function field arithmetic: integral $t$-motivic cohomology governs linear relations among Carlitz polylogarithms, its torsion is expressed in terms of the denominator of Bernoulli-Carlitz numbers and the Fitting ideal of class modules is a special zeta value. We also express the regulator of $\underline{A}(n)$ for positive $n$ in terms of generalized Carlitz polylogarithms; after establishing their algebraic relations using difference Galois theory together with the Anderson-Brownawell-Papanikolas criterion, we prove that the regulator is an isomorphism if, and only if, $n$ is prime to the characteristic.
