The Hasse norm principle for abelian extensions
The Hasse norm principle for abelian extensions
复制标题
阿贝尔扩张的哈斯范数原理
DOI：
10.1353/ajm.2018.0048
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发表时间：
2015
影响因子：
1.7
通讯作者：
Rachel Newton
中科院分区：
文献类型：
--
作者：
C. Frei;D. Loughran;Rachel Newton
文摘：研究了不符合Hasse范数原理的数域$k$的有界判别式的阿贝尔扩张的分布。例如，我们对有限交换群$G$进行分类，对于这些有限交换群，$G$-$k$的扩张的正比例不符合Hasse范数原理。对于伴随范数一环的弱逼近失败，我们得到了类似的分类。这些结果涉及对施加了无限多个局部条件的有界判别式的阿贝尔扩张进行计数，这是我们在Wright工作的基础上，使用调和分析中的工具实现的。
Abstract:We study the distribution of abelian extensions of bounded discriminant of a number field $k$ which fail the Hasse norm principle. For example, we classify those finite abelian groups $G$ for which a positive proportion of $G$-extensions of $k$ fail the Hasse norm principle. We obtain a similar classification for the failure of weak approximation for the associated norm one tori. These results involve counting abelian extensions of bounded discriminant with infinitely many local conditions imposed, which we achieve using tools from harmonic analysis, building on work of Wright.