p無窮循環擴張上之依烏阿沙娃理論

Abstract

1950年代，對於數域上的某些擴張，岩澤提出了計算其 class number 的理論。並討論了 cyclotomic 擴張及其他種類的伽羅瓦擴張。在這篇文章中，我將介紹這個定理並給出一些例子。

In the 1950's, Kenkichi Iwasawa had constructed his class number formula on extensions of number fields. Iwasawa investigated towers of cyclotomic fields and other kinds of Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. In this thesis, I would like to introduce this theory and give some examples.