We construct an analogue of the classical descent theory of Colliot-Thélène and Sansuc in which algebraic tori are replaced with finite supersolvable groups. As an application, we show that rational points are dense in the Brauer–Manin set for smooth compactifications of certain quotients of homogeneous spaces by finite supersolvable groups. For suitably chosen homogeneous spaces, this implies the existence of supersolvable Galois extensions of number fields with prescribed norms, generalising work of Frei, Loughran and Newton.

中文翻译：

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有理点的超可解下降

我们构建了 Colliot-Thélène 和 Sansuc 的经典下降理论的类似物，其中代数环被替换为有限超可解群。作为一个应用，我们证明了有理点在布劳尔-马宁集中是密集的，用于通过有限超可解群平滑压缩齐次空间的某些商。对于适当选择的齐次空间，这意味着存在具有规定范数的超可解的数域伽罗瓦扩展，概括了弗雷、洛夫兰和牛顿的工作。