Please use this identifier to cite or link to this item: https://ah.nccu.edu.tw/handle/140.119/56880


Title: 投射有限群表現之形變理論
Deformation Theory of Representations of Profinite Groups
Authors: 周惠雯
Chou, Hui Wen
Contributors: 余屹正
Yu, Yih Jeng
周惠雯
Chou, Hui Wen
Keywords: 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
Date: 2012
Issue Date: 2013-02-01 16:53:18 (UTC+8)
Abstract: 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.
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Description: 碩士
國立政治大學
應用數學研究所
99751014
101
Source URI: http://thesis.lib.nccu.edu.tw/record/#G0099751014
Data Type: thesis
Appears in Collections:[應用數學系] 學位論文

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