有理点的超解下降

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-02-26 DOI:10.2140/ant.2024.18.787

Yonatan Harpaz, Olivier Wittenberg

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引用次数: 0

摘要

我们构建了科利奥-泰莱（Colliot-Thélène）和桑苏克（Sansuc）经典后裔理论的类似理论，其中代数环被有限可超溶群取代。作为应用，我们证明了在有限超可溶群对某些均相空间商的光滑压实中，有理点在布劳尔-马宁集中是密集的。对于适当选择的均质空间，这意味着存在具有规定规范的数域超可溶伽罗瓦扩展，这是对弗雷、拉夫兰和牛顿工作的推广。

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Supersolvable descent for rational points

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.

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来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.