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    题名: 投射有限群表現之形變理論
    Deformation Theory of Representations of Profinite Groups
    作者: 周惠雯
    Chou, Hui Wen
    贡献者: 余屹正
    Yu, Yih Jeng
    周惠雯
    Chou, Hui Wen
    关键词: 投射有限群
    表現
    形變
    泛形變
    泛形變環
    扎里斯基切空間
    Profinite groups
    Representations
    Deformations
    Universal deformations
    Universal deformation rings
    Zariski tangent space
    Group cohomology
    日期: 2012
    上传时间: 2013-02-01 16:53:18 (UTC+8)
    摘要: 在本碩士論文中, 我們闡述了投射有限群表現, 以及其形變理論。 我們亦特別研究這些表示在 GL_1 和 GL_2 之形變, 並且給了可表示化 的判定準則。 最後, 我們解釋相對應的泛形變環之扎里斯基切空間與 群餘調之關連, 並計算了 GL_1 的泛形變表現。
    In this master thesis, we give an exposition of the deformation theory of representations for GL_1 and GL_2, respectively, of certain profinite groups. We give rigidity conditions of the fixed representation and verify several conditions for the representability. Finally, we interpret the Zariski tangent spaces of respective universal deformation rings as certain group cohomology and calculate the universal deformation for GL_1.
    參考文獻: [1] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969.
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    [10] A. Grothendieck and J. Dieudonne ́, El ́ements de G ́eom ́etrie Alg ́ebrique, Publ. Math. IHES,4 (1960), 8 (1961), 11 (1961), 17 (1963), 20 (1964), 24 (1965), 28 (1966), 32 (1967).
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    描述: 碩士
    國立政治大學
    應用數學研究所
    99751014
    101
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    数据类型: thesis
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