can somebody tell me in simple words that what is the idea with class field theory and what is it about?

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- Feb 12th 2009, 01:38 PMpeteryellowclass field theory
can somebody tell me in simple words that what is the idea with class field theory and what is it about?

- Feb 12th 2009, 08:24 PMThePerfectHacker
It K/F is a Kummer extension then there is a nice way to think of K i.e. K is an adjunction of n-th roots of F. But in order to be a Kummer extension we need F to have enough roots of unity, in fact, it must contain all roots of unity of n. The idea of class field theory is to remove or at least ease the restriction that F has to contain all the roots of unity and try to generalize the notions of Kummer extensions. (Nod)