請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30653完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 康明昌(Ming-Chang Kang) | |
| dc.contributor.author | Chih-Chieh Chen | en |
| dc.contributor.author | 陳志傑 | zh_TW |
| dc.date.accessioned | 2021-06-13T02:11:19Z | - |
| dc.date.available | 2007-07-03 | |
| dc.date.copyright | 2007-07-03 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-06-25 | |
| dc.identifier.citation | [Ar] J.K. Arason, Cohomologische Invarianten quadratischer Formen, J. Algebra 36 (1975), no. 3, p.448 - p.491.
[BF] G.Berhuy and G.Favi, Essential dimension: a functorial point of view after A. Merkurjev, Documenta Math. 8 (2003), 279-330. [BR] J. Bulher and Z. Reichstein, on the essential dimension of a finite group, Compositio Math. 106(1997), 159-179 [CHKZ] H.Chu, S.J. Hu, M. Kang and J. Zhang, Groups with essential dimension one. preprint. [De] A. Delzant, D'efinition des classes de Stiefel-Whitney d'un module quadratique sur un corps de caract'eristique diff'erente de 2. C.R Acad. Sci. Paris 255. [Fl] M. Florence, On the essential dimension of cyclic p-groups , preprint. [GMS] R. Garibaldi, A. Merkurjev, J.-P. Serre, Cohomological invariants in Galois cohomology. AMS University Lecture Series 28 (2003). [JLY] C. Jensen, A. Ledet and N. Yui, Generic polynomials: constructive aspects of the inverse Galois problem, MSRI Publ. vol. 45, Cambridge University Press, Camgridge, 2002. [Ka] M. Kang, Essential dimension of finite groups. preprint. [KMRT] M. Knus, A. Merkurjev, M. Rost and J-P Tignol, the book of involutions , American Mathematical Society Colloquium Publications, vol.44 (1998). [Mu] D. Mumford, Abelian varieties, Tata Institute of Fundamental Research, Bombay, reprinted. 1985. [Re] Z. Reichstein, On the Notion of Essential Dimension for Algebraic Groups , Transformation Groups, 5, no. 3 (2000), 265-304. [Se1] J.-P. Serre, Galois cohomology, Springer Monographs in Mathematics, 1997. [Se2] J.-P. Serre, Local fields, Graduate Texts in Mathematics 67, 1979. [Sh] S.S. Shatz, Group schemes, formal groups, and $p$-divisible groups. Appeared in Arithmetic geometry (Storrs, Conn., 1984), 29--78, Springer, New York, 1986. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30653 | - |
| dc.description.abstract | 在九零年代初期 J.Bulher and Z.Reichstein 開始考慮有限群的「必要維度」，不久之後進而考慮代數群的必要維度。 大約在十年之前人們了解到所謂的必要維度是可以用上同調代數的方法定義的， Berhuy and Favi 的論文 [BF] 就是整理 Merkurjev 在這方面的工作。我的目標是簡單介紹這兩種定義; 第一篇是關於 affine group scheme 的基本介紹，而在第二章和第三章我會清楚地介紹這兩種定義以及目前能得到的結果; 最後我用基本的 Galois theory 來證明這兩種定義是等價的。
這篇論文大部份的內容是重新整理 [KMRT], [BF], and [Ka] 裡頭關於必要維度的結果，而引理 1.1.2 以及命題 3.4.1是由我獨立完成的。 | zh_TW |
| dc.description.abstract | The name 'essential dimension' was given by J.Bulher and Z.Reichstein [BR] and Z.Reichstein [Re] (see also [Ka]); Berhuy and Favi [BF] gives a functorial definition following Merkurjev. In this thesis, my goal is to show that this two definitions are equivalent; in Chapter 1 I'll recall some basic facts of affine group scheme; in Chapter 2 and Chapter 3 both two definitions of essential dimension will be mentioned; finally, in Chapter 3 I'll prove such definitions are compatible.
The thesis is re-organization of contents of [KMRT], [BF], and [Ka] , and Lemma 1.1.2 and Proposition 3.4.1 are proven by myself. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T02:11:19Z (GMT). No. of bitstreams: 1 ntu-96-R94221005-1.pdf: 345347 bytes, checksum: e1f89bc5e55a2117aa004587905a1315 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | 1. Group Scheme.........1
1.1 Basic Definitions......................................1 1.2 Exact Sequence of Affine Group Schemes.................7 2.Essential Dimension: Functorial Definition...............9 2.1 Essential Dimension of Functors........................9 2.2 Essential Dimension of Group Schemes..................13 2.3 Cohomological Invariants..............................19 3. Essential Dimension of Finite Groups..........23 3.1 Basic Definitions............................23 3.2 Main Technique...............................25 3.3 Symmetric Groups and Alternating Groups......31 3.4 Proof of Equivalent Definition...............34 3.5 Final Remark.................................36 Bibliography.....................................37 | |
| dc.language.iso | en | |
| dc.title | 有限群的必要維度 | zh_TW |
| dc.title | Essential Dimension of Finite Groups | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 朱樺(Huah Chu),胡守仁(Shou-Jen Hu) | |
| dc.subject.keyword | 有限群,必要維度, | zh_TW |
| dc.subject.keyword | finite groups,essential dimension,affine group scheme,Galois cohomology, | en |
| dc.relation.page | 38 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-06-26 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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