谢瓦莱在类域论方面的贡献

The Contribution of Chevalley to the Class Field Theory

回顾了类域论的早期发展,尤其是希尔伯特的研究;以谢瓦莱引入的伊代尔概念为核心,深刻挖掘伊代尔概念的重要性,重新评价了谢瓦莱类域论工作的历史价值。指出正是借助伊代尔的概念,谢瓦莱摒弃了解析工具,完成了类域论的算术化过程,也建立了伊代尔叙述的整体类域论,更重要的是,将拓扑、泛函与类域论结合起来,促进了类域论的发展。这些研究对我们更全面、深刻的认识谢瓦莱的工作有借鉴意义。

The early development of the class field theory is reviewed,particularly Hilbert＇s research.With Chevalley＇s idele conception at the core and based on the exploration of its importance,the historical significance of Chevalley＇s work is re-evaluated.This paper concludes that it is the conception of idele that makes Chevalley accomplish the global class field theory,as well as the purely arithmetic proof of the class field theory without analysis.More importantly,by means of the idele conception,Chevalley＇s work integrates topology and functional analysis together,thus providing some reference for the perspective on Chevalley＇s work.