##  [Artin Map](/artin-map) 

  ##  [Artin Map](https://puremath.quantumdictionary.io/artin-map-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The canonical reciprocity homomorphism from the idèle class group (or ideal class group) of a global or local field to its abelianized Galois group that records Frobenius or geometric action of primes and realizes class field theory's correspondence between abelian extensions and class groups.