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希爾伯特第十二問題

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希爾伯特第十二問題(英語:Hilbert's twelfth problem)是希爾伯特的23個問題之一,將只適用有理数阿贝耳扩张英语Abelian extension克罗内克-韦伯定理英语Kronecker–Weber theorem,擴展到任意的代數數域。利用複乘英语complex multiplication已可將克罗内克-韦伯定理延伸到虛二次域。進一步的擴展(克羅內克的青春夢(德語:Kronecker Jugendtraum))到2008年為止尚未解決。一般認為十九世紀德國數學家利奧波德·克羅內克Leopold Kronecker)將這個和複乘有關的問題視為「年輕時最親愛的夢想」(liebster Jugendtraum)。

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希爾伯特第十二問題
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