带实素点的算术陈-西蒙斯理论
Arithmetic Chern-Simons theory with real places
AI总结：
本文将全虚数域上的算术陈-西蒙斯理论推广到带实素点的任意数域，借助紧支撑上同调处理实素点，并基于已有结果用扭论证构造了带一般系数的非阿贝尔规范群下的非平凡算术陈-西蒙斯不变量新例子。
摘要：
本文的研究目标有两方面：一是将[Kim15, CKK+16]中研究的全虚数域上的算术陈-西蒙斯理论推广到任意（带实素点的）数域；二是给出与非阿贝尔规范群相关、系数为$\n\n\mathbb{Z}/n\mathbb{Z}$（$n \geq 2$）的非平凡算术陈-西蒙斯不变量的新例子。推广的核心思路是利用带紧支撑的上同调（见[Mil06]）来处理实素点。在本文结果之前，非平凡例子仅限于[CKK+16]中系数为$\mathbb{Z}/2\mathbb{Z}$的部分非阿贝尔规范群情形，以及[BCG+18]中系数为$\mathbb{Z}/n\mathbb{Z}$的阿贝尔循环规范群情形。我们的（带非阿贝尔规范群和一般系数$\mathbb{Z}/n\mathbb{Z}$的）非平凡例子，将基于[BCG+18]的例子通过简单的扭论证给出。
英文摘要：
The goal of this paper is two-fold: we generalize the arithmetic Chern-Simons theory over totally imaginary number fields studied in [Kim15, CKK+16] 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 (see [Mil06]) to deal with real places. Before the results of this paper, non-trivial examples were limited to some non-abelian gauge group with coefficient $\mathbb{Z}/2\mathbb{Z}$ in [CKK+16] and the abelian cyclic gauge group with coefficient $\mathbb{Z}/n\mathbb{Z}$ in [BCG+18]. 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 based on examples of [BCG+18].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
