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The Artin Isomorphism

  • Harvey Cohn
Part of the Universitext book series (UTX)

Abstract

We now define an isomorphism between the class groups H = H{J}= J p /J and G = Gal K/k. It shall do more than map elements of each group into one another; it shall be covariant under automorphisms of the lower field k (over say ℚ). This isomorphism is due to Artin [1924]. It was discovered in an analytic context (which we discuss in the next chapter), but, for now, we see the isomorphism as a unifying point and point of departure for class field theory.

Keywords

Prime Ideal Class Field Ideal Class Class Field Theory Residue Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1978

Authors and Affiliations

  • Harvey Cohn
    • 1
  1. 1.City CollegeCity University of New YorkNew YorkUSA

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