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I've noticed that there seem to be two approaches to learning class field theory. The first is to first learn about local fields and local class field theory, and then prove the basic theorems about ...

Let $F$ be a global field without real places (that is, a function field or a totally imaginary number field). Let $K/F$ be a cyclic extension of degree $n$. Let $S$ be a ${\rm Gal}(K/F)$-invariant ...