当前位置:
X-MOL 学术
›
J. Number Theory
›
论文详情
Our official English website, www.x-mol.net, welcomes your
feedback! (Note: you will need to create a separate account there.)
The norm residue symbol for higher local fields
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-07-22 , DOI: 10.1016/j.jnt.2021.06.031 Jorge Flórez 1
中文翻译:
较高局部场的范数残差符号
更新日期:2021-07-22
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-07-22 , DOI: 10.1016/j.jnt.2021.06.031 Jorge Flórez 1
Affiliation
In this paper we investigate the Kummer pairing associated to an arbitrary (one-dimensional) formal group. In particular, we obtain formulae describing the values of the pairing in terms of multidimensional p-adic differentiation, the logarithm of the formal group, the generalized trace and the norm on Milnor K-groups. The results are a generalization to higher-dimensional local fields of Kolyvagin's explicit reciprocity laws. In particular, they constitute a generalization of the reciprocity laws of Artin-Hasse, Iwasawa and Wiles.
中文翻译:
较高局部场的范数残差符号
在本文中,我们研究了与任意(一维)形式群相关的 Kummer 配对。特别是,我们获得了用多维p进微分、形式群的对数、广义迹线和 Milnor K 群的范数来描述配对值的公式。结果是对 Kolyvagin 显式互易律的高维局部域的推广。特别是,它们构成了对 Artin-Hasse、Iwasawa 和 Wiles 互惠定律的概括。