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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/83372


    Title: 有關數體的低階加羅瓦同調群
    Various Results on Low Galois Gohomology Groups of Number Fields
    Authors: 康瓊如
    Kan, Chiung Ju
    Contributors: 陳永秋
    康瓊如
    Kan, Chiung Ju
    Keywords: 低階加羅瓦
    同調
    Gohomology
    Galois
    Date: 2002
    Issue Date: 2016-03-31 16:39:15 (UTC+8)
    Abstract: 　　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.
    Reference: E. Artin and J. Tate, Class Field Theory, W. A. Benjamin,
    Inc., New York, 1967.
    E. Artin, Galois Theory (Notre Dame Math. Lectures, No. 2),
    Indiana, 1946.
    A. Babakhanian, Cohomological methods in group theory,
    Marcel Dekker, New York, 1972.
    M. Baker, An introduction to class field theory, Preprint, U. C. Berkeley, 1996.
    R. J. Bond, On the splitting of the Hilbert class field,
    Journal of Number Theory 42, 1992, 349-360.
    R. J. Bond, Some results on the capitulation problem,
    J. Number Theory 13, 1981, 246-254.
    Brumer and Rosen, Class number and ramification in number fields, Nagoya Math.J. 1963,97-101.
    H. Cohn, A classical invitation to algebraic numbers and class fields, Universitext, Springer-Verlag, Berlin and New York, 1978.
    G. Cornell and M. Rosen, A note on the splitting of the Hilbert
    class field, Journal of Number Theory 28, 1988, 152-158.
    D. Garbanati, Extension of the Hasse norm theorem, Bull.
    Amer. Math. Soc. 81, 1975, 583-586.
    R. Gold, Hilbert class fields and split extensions, Illinois
    J. Math. 21, 1977, 66-69.
    M. Hall, The theory of groups, Macmillan, New York, 1959.
    F. P. Heider, Zahlentheoretische Knoten unendlicher Erweiterungen,
    Archiv der Math. 37, 1981, 341-352.
    C. S. Herz, Construction of class fields, Seminar on Complex
    Multiplication}, Chap. 7, Springer Verlag, New York, 1966.
    M. Ishida, Some unramified abelian extensions of algebraic number fields, J. Reine Angew. Math. 268/269, 1974, 165-173.
    K. Iwasawa, A note on the group of units of an algebraic number
    field, J. Math Pures Appl. 35, 1956, 189-192.
    J. P. Jans, Rings and Homology, Holt, Rinehart and winston,
    Inc. New York, 1964.
    W. Jehne, On knots in algebraic number theory, J. reine u.
    angew. Math. 311, 1979, 215-252.
    H. Kisilevsky, Number fields with class number congruent to 4 mod
    8 and Hilbert`s theorem 94, J. Number Theory 8, 1976,
    271-279.
    H. Kisilevsky, Some results related to Hilbert`s theorem 94,
    J. Number Theory 2, 1970, 199-206.
    F. Lemmermeyer, Construction of Hilbert 2-class fields,
    Preprint, Heidelberg, 1991.
    F. Lorenz, Ein Scholion zum Satz 90 von Hilbert, Abh. Math.
    Sem. Univ. Hamburg 68,1998.
    S. Maclane, Homology, Springer Verlag, Berlin, 1963.
    K. Miyake, The Capitulation Problem, Sugaku Expositions,
    Vol. 1, Number 2, 1988, 175-194.
    J. Tate, The higher dimensional cohomology
    groups of class field theory, Ann. of Math. 56, 1952,
    294-297.
    E. Weiss, Cohomology of groups, Academic Press, New York,
    1969.
    B. F. Wyman, Hilbert class fields and group extensions,
    Scripta Mathematica, Vol 29, 1973, 141-149.
    K. Yamamura, The maximal unramified extensions of the imaginary quadratic number fields with class number two, Journal of number theory 60, 1996, 42-50.
    Description: 碩士
    國立政治大學
    應用數學系
    88751005
    Source URI: http://thesis.lib.nccu.edu.tw/record/#B2002000059
    Data Type: thesis
    Appears in Collections:[Department of Mathematical Sciences] Theses

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