coGalois理论的一个更一般的框架
A more general framework for coGalois theory
摘要：
这篇论文是在国际会议上发表的演讲的扩展版本：代数，几何和拓扑学的实验和理论方法，于2013年6月21日至24日在Eforie Nord（罗马尼亚）举行。它的目的是为场论中一个相当新的理论提供一个更一般的框架，这个理论被称为co伽罗瓦论，它与非常经典的伽罗瓦论有些对偶，而且比库默尔理论更一般。在这个更一般的框架的主要调查对象是coGalois连接自然地与任何三重$\,(Γ, \frak{G}, η)\,$，其中$\,Γ\,$是一个投射有限群，$\,\frak{G}\,$是一个profinite运营商$\,Γ$ -组，和$\,η: Γ\longrightarrow \frak{G}\,$是一个连续的$\,1$ -cocycle的属性，投射有限群$\,\frak{G}\,$是拓扑生成的图像$\,η(Γ)$。
英文摘要：
The paper is an extended version of a talk given at the International Conference: Experimental and Theoretical Methods in Algebra, Geometry and Topology, which took place June 21--24, 2013 in Eforie Nord (Romania). Its purpose is to present a more general framework for a fairly new theory in Field Theory, called coGalois Theory, which is somewhat dual to the very classical Galois Theory and is more general than the Kummer Theory. The main object of investigation in this more general framework is the coGalois connexion naturally associated to any triple $\,(Γ, \frak{G}, η)\,$, where $\,Γ\,$ is a profinite group, $\,\frak{G}\,$ is a profinite operator $\,Γ$-group, and $\,η: Γ\longrightarrow \frak{G}\,$ is a continuous $\,1$-cocycle with the property that the profinite group $\,\frak{G}\,$ is topologically generated by the image $\,η(Γ)$.
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