Explicit Class Field Theory for Kummer Extensions

Abstract

在本碩士論文中，我們首先介紹一些已經知道的結果。接著定義一個pairing並且利用之前介紹的結果去討論pairing的性質。最後利用這個pairing直接討論class field theory for Kummer extensions 而不套用古典的local class field theory。In this thesis, we first introduce some known results. Then we define a pairing and use the known results to discuss properties of this pairing. Finally, we use this pairing to discuss local class field theory for Kummer extension without employing the classical local class field theory.