數體的低階加羅瓦同調群是最近數論裡面的一大研究主題，本文的第一部分深入討論有關這個主題的一些古典的及最近的結果以及實際的例子，一個重要的主題是有關數體的希爾伯類體所定義的擴張群是否可分解，陳氏的方法應用數結這個概念可證明一些在文獻上所得到的結果。本文深入的探討這些數結而獲得在冪零群上完成的結果。利用這方法可望推廣到可解群的問題上。 / Low Galois cohomology groups of number fields are studied intensively in recent literature which in the first part of this thesis will be revisited with emphasis of giving direct and rigorous definitions and with providing concrete examples, classical and from more recent results from the literature. One important topic is the splitting problem of group extensions induced by the Hilbert class field of a given Galois extension of number fields. Following Tan's approach which relates the splitting problem to the triviality of certain number knots, we elaborate known results on criteria for the splitting by giving new proofs which make use of number knots; we also give a complete result in the case of a nilpotent Galois extension. The case of solvable Galois extensions seems possibly settled using our approach.
| Identifer | oai:union.ndltd.org:CHENGCHI/B2002000059 |
| Creators | 康瓊如, Kan, Chiung Ju |
| Publisher | 國立政治大學 |
| Source Sets | National Chengchi University Libraries |
| Language | 英文 |
| Detected Language | English |
| Type | text |
| Rights | Copyright © nccu library on behalf of the copyright holders |
Page generated in 0.0223 seconds