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Tower of the maximal abelian extensions of local fields and its application

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Abstract

In this paper, we study the algebraic structure of principal units in the tower of the maximal abelian extensions of local fields of characteristic zero and the corresponding Galois groups at each level. As an application, we show the finiteness result for the number of coverings with a given degree of the maximal abelian extension of a local field in characteristic zero. The number of p-coverings for \({\mathbb{Q}_p}\) is computed explicitly.

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Authors and Affiliations

  1. Academy of Mathematics and System Science, CAS, 100190, Beijing, People’s Republic of China

    Dasheng Wei & Fei Xu

  2. School of Mathematics, Capital Normal University, 100037, Beijing, People’s Republic of China

    Fei Xu

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  1. Dasheng Wei
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  2. Fei Xu
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Correspondence to Fei Xu.

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Wei, D., Xu, F. Tower of the maximal abelian extensions of local fields and its application. manuscripta math. 129, 1–28 (2009). https://doi.org/10.1007/s00229-009-0252-9

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  • DOI: https://doi.org/10.1007/s00229-009-0252-9

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