Non-abelian class field theory

In mathematics, non-abelian class field theory is a catchphrase, meaning the extension of the results of class field theory, the relatively complete and classical set of results on abelian extensions of any number field K, to the general Galois extension L/K. While class field theory was essentially known by 1930, the corresponding non-abelian theory has never been formulated in a definitive and accepted sense.^[1]

^ The problem of creating non-Abelian class field theory for normal extensions with non-Abelian Galois group remains. From Kuz'min, L.V. (2001) [1994], "Class field theory", Encyclopedia of Mathematics, EMS Press.

[1] The problem of creating non-Abelian class field theory for normal extensions with non-Abelian Galois group remains. From Kuz'min, L.V. (2001) [1994], "Class field theory", Encyclopedia of Mathematics, EMS Press.

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