20世纪30年代谢瓦莱对类域论的重建

Chevalley’s Reconstruction of Class Field Theory in the 1930s

本文分析了谢瓦莱在20世纪30年代的类域论工作,指出其对类域论的算术化证明并不是一蹴而就的,甚至对类域论的算术化还产生过怀疑,但最后巧妙地借助伊代尔的概念将类域论完全算术化,使之成为代数数论中体系最完美的一种。以谢瓦莱和哈塞等人的通信为主要资料,论述了诺特、哈塞和阿廷等德国数学家与谢瓦莱的学术关系,以及他们对谢瓦莱工作的评价,并阐述了当时法国和德国的数学研究取向之不同。

Focusing on Chevalley’s works on class field theory, this paper points out that the arithmetical demonstration of class field theory was not accomplished in one step. Chevalley was, in fact, initially skeptical about the arithmetization of class field theory, however, he eventually proved it with the concept of idéle in 1940. On the basis of correspondence between Chevalley, Hasse and other German mathematicians, this paper also outlines the academic relationship between Chevalley and German mathematicians, and the evaluation of German and French mathematicians of Chevalley’s work on class field theory at the time.