论文标题
理性点可超过下降
Supersolvable descent for rational points
论文作者
论文摘要
我们构建了Colliot-Thélène和Sansuc的经典血统理论的类似物，其中代数托里被有限的Supersolwight群代替。作为一种应用，我们表明，在有限的超偏群中，有理点在Brauer-Manin设置的设置中，以平滑某些同质空间的商品。对于适当选择的均匀空间，这意味着存在具有规定规范的数字领域的可超过的galois扩展，从而概括了弗雷·拉夫兰·纽顿的工作。
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-Newton.
