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dbr:Non-abelian_classfield_theory
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Non-abelian class field theory 非可換類体論
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数学において、非可換類体論（ひかかんるいたいろん、英: non-abelian class field theory）は、類体論の結果、任意の代数体 K のアーベル拡大についての比較的完全で古典的な一連の結果の、一般のガロワ拡大 L/K への拡張を意味するキャッチフレーズである。拡大の群が可換な場合の理論である類体論は1930年頃には本質的には知られるところとなったが、それを非可換の場合に拡張する理論は、まだ誰もが認める確定した定式化には至っていない。 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.
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数学において、非可換類体論（ひかかんるいたいろん、英: non-abelian class field theory）は、類体論の結果、任意の代数体 K のアーベル拡大についての比較的完全で古典的な一連の結果の、一般のガロワ拡大 L/K への拡張を意味するキャッチフレーズである。拡大の群が可換な場合の理論である類体論は1930年頃には本質的には知られるところとなったが、それを非可換の場合に拡張する理論は、まだ誰もが認める確定した定式化には至っていない。 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.
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