The Artin Isomorphism

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


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.


Prime Ideal Class Field Ideal Class Class Field Theory Residue Symbol 
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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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