The works of Claude Chevalley on class field theory: an introduction
type: Item
instance of: scholarly article
title: The works of Claude Chevalley on class field theory: an introduction
zbMATH Open document ID: 1172.11041
author: Shōkichi Iyanaga
published in: Japanese Journal of Mathematics. 3rd Series
publication date: 2009-02-06T00:00:00Z
review text: In this paper, the author explains the contribution of C. Chevalley to class field theory. After giving the development of a series of mathematical ideas, from Gauss and Hilbert to Takagi and Artin, that moved Chevalley to create his remarkable works; the author shows that Chevalley's main achievements on the subject were the first arithmetic proof of the local class field theory without depending on the global theory, arithmetization of the global class field theory, and its generalization and presentation for infinite extensions by introducing ideles which are now a kind of natural language in algebraic number theory. This paper is a very good introduction to the detailed works of Chevalley.
reviewed by: Abdelmalek Azizi
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 01A70
zbMATH DE Number: 5503381
zbMATH Keywords: ideles
zbMATH Keywords: class field theory
MaRDI profile type: Publication
full work available at URL: s11537-006-0502-5
OpenAlex ID: W2087811318
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DOI: 10.1007/S11537-006-0502-5
description: scientific article; zbMATH DE number 5503381