Various Results on Low Galois Gohomology Groups of Number Fields
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...
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| Format: | Others |
| Language: | en_US |
| Published: |
2002
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| Online Access: | http://ndltd.ncl.edu.tw/handle/36964699336917622942 |
| Summary: | 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.
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