Various Results on Low Galois Gohomology Groups of Number Fields

• Main Authors: Chiung-ju Kan, 康瓊如
• Other Authors: 陳永秋老師
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/36964699336917622942

碩士 === 國立政治大學 === 應用數學系 === 90 === 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.