A Quick Tour of Class Field Theory

  • Dinakar Ramakrishnan
  • Robert J. Valenza
Part of the Graduate Texts in Mathematics book series (GTM, volume 186)


One could argue that the principal goal of number theory is to understand the integral or rational solutions of systems of Diophantine equations; that is, polynomial equations with integral coefficients. Nineteenth-century mathematicians, mainly riding the impetus provided by attempts to tackle the Fermat equation x n +y n =z n (n≥3), realized the benefits of studying the solutions in extended number systems R, as opposed to confining one’s attention to only Z and Q, and this led eventually to global and local fields and their rings of integers.


Conjugacy Class Galois Group Open Subgroup Residue Field Global Field 
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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Dinakar Ramakrishnan
    • 1
  • Robert J. Valenza
    • 2
  1. 1.Mathematics DepartmentCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of MathematicsClaremont McKenna CollegeClaremontUSA

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