Arithmetic Chern-Simons theory with real places
Arithmetic Chern-Simons theory with real places
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实数地方的算术陈-西蒙斯理论
DOI：
10.1142/s021821652350027x
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发表时间：
2019
影响因子：
0.5
通讯作者：
Jeehoon Park
中科院分区：
文献类型：
--
作者：
Jungin Lee;Jeehoon Park
本文的目标是两个折叠：我们推广的算术Chern-Simons理论在全虚数域到任意数域（与真实的地方），并提供新的例子，非平凡的算术Chern-Simons不变量与系数$\mathbb {Z}/n\mathbb{Z}$ $（n \geq 2）$关联到一个非阿贝尔规范群。推广的主要思想是利用具有紧支集的上同调来处理真实的库所。到目前为止，非平凡的例子仅限于系数为$\mathbb{Z}/2\mathbb {Z}$的非阿贝尔规范群和系数为$\mathbb{Z}/n\mathbb{Z}$的阿贝尔循环规范群。我们的非平凡的例子与非阿贝尔规范群和一般系数$\mathbb{Z}/n\mathbb{Z}$将通过一个简单的扭曲的论点。在附录中，我们解释了替代方法的推广的基础上，Zink和Conrad-Masullo的工作。
The goal of this paper is two folds: we generalize the arithmetic Chern-Simons theory over totally imaginary number fields to arbitrary number fields (with real places) and provide new examples of non-trivial arithmetic Chern-Simons invariant with coefficient $\mathbb{Z}/n\mathbb{Z}$ $ (n \geq 2)$ associated to a non-abelian gauge group. The main idea for the generalization is to use cohomology with compact support to deal with real places. So far, the non-trivial examples are limited to some non-abelian gauge group with coefficient $\mathbb{Z}/2\mathbb{Z}$ and the abelian cyclic gauge group with coefficient $\mathbb{Z}/n\mathbb{Z}$. Our non-trivial examples with non-abelian gauge group and general coefficient $\mathbb{Z}/n\mathbb{Z}$ will be given by a simple twisting argument. In the appendix, we explain alternative method of generalization based on the work of Zink and Conrad-Masullo.