Hasse principles for multinorm equations
Hasse principles for multinorm equations
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DOI：
10.1016/j.aim.2019.106818
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发表时间：
2015-07
影响因子：
1.7
通讯作者：
E. Bayer-Fluckiger;Ting-Yu Lee;R. Parimala
中科院分区：
文献类型：
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作者：
E. Bayer-Fluckiger;Ting-Yu Lee;R. Parimala
哈塞的一个经典结果指出，范数原理对全局域的有限循环扩张成立，换句话说，局部范数是全局范数。我们研究了整体域上有限维交换代数的范数原理;由于这样的代数是可分扩张的乘积，这通常被称为多项式原理。在假设étale代数含有循环因子的条件下，利用有限交换群的显式构造元，给出了Hasse原理成立的一个充要条件.这可以被看作是布劳尔-马宁对哈塞原理的阻碍的明确描述。
A classical result of Hasse states that the norm principle holds for finite cyclic extensions of global fields, in other words local norms are global norms. We investigate the norm principle for finite dimensional commutative étale algebras over global fields; since such an algebra is a product of separable extensions, this is often called the multinorm principle. Under the assumption that the étale algebra contains a cyclic factor, we give a necessary and sufficient condition for the Hasse principle to hold, in terms of an explicitly constructed element of a finite abelian group. This can be seen as an explicit description of the Brauer-Manin obstruction to the Hasse principle.