unramified prime divisor

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Takagi existence theorem — In class field theory, the Takagi existence theorem states that for any number field K there is a one to one inclusion reversing correspondence between the finite abelian extensions of K (in a fixed algebraic closure of K ) and the generalized… … Wikipedia
Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. Contents 1 Local… … Wikipedia

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