Mathematical  Culture and Thought

Mathematical Culture and Thought

A History of Class Field Theory

Document Type : Review

Authors
Department of Mathematical Sciences‎, ‎Sharif University of Technology‎, ‎Iran
Abstract
In this ‎paper‎‎, ‎we study the historical background of class field theory‎. ‎First‎, ‎we investigate Kummer's theory‎, ‎which is one of the algebraic backgrounds of class field theory‎. ‎Then we turn to Comer's youthful dream that led to the question of finding all Abelian extensions of number fields‎. ‎After this‎, ‎we state Takagi's theorems and finally study Hilbert's problems‎. ‎By examining the historical course of the above‎, ‎we are trying to present a better picture of the historical background of class field theory‎, ‎which is one of the basic foundations of mathematics.
Keywords

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Volume 42, Issue 2 - Serial Number 73
December 2023
Pages 313-342

  • Receive Date 09 August 2023
  • Accept Date 21 November 2023
  • Publish Date 22 December 2023