 Existence theorem of global class field theory (source code)

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= Existence theorem of global class field theory

Finite abelian extensions of $K$ correspond contravariantly to congruence subgroups $H$ with $P_K(\mathfrak m)\subseteq H\subseteq I_K(\mathfrak m)$, and the Artin map identifies $I_K(\mathfrak m)/H$ with the Galois group.

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