JP Journal of Algebra, Number Theory and Applications
Volume 16, Issue 1, Pages 81 - 88
(February 2010)
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ON THE NORM THEOREM OF CYCLIC EXTENSIONS
Tomio Kubota
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Abstract: Let �be a cyclic extension over an algebraic number field F, �and �be the idele class group and the connected component of the unity of �respectively. Furthermore, let �be the Galois group of the maximal abelian extension over K. Then, our main theorem says that �the norm theorem of �is derived from the class field isomorphism �Usually, the norm theorem is proved in the process of constructing the class field theory. But, our result has its own meaning, since it gives us a way to a new, geometric foundation of the class field theory. |
Keywords and phrases: class field theory, geometry of numbers. |
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