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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4715完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.author | Chien-Hua Chen | en |
| dc.contributor.author | 陳健樺 | zh_TW |
| dc.date.accessioned | 2021-05-14T17:45:45Z | - |
| dc.date.available | 2015-07-20 | |
| dc.date.available | 2021-05-14T17:45:45Z | - |
| dc.date.copyright | 2015-07-20 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-07-06 | |
| dc.identifier.citation | D.Mumford, Abelian Varieties, Oxford University Press, 1970
J.H.Silverman, The Arithmetic of Elliptic Curves, Springer GTM 106, 1986 J.Milnor and D.Husemoller, Symmetric Bilinear Forms, Springer Ergebnisse 73, 1970 J.P.Serre, Galois Cohomology, Springer Monographs in Mathematics, 1997 M.Bhargava and B.H.Gross, Arithmetic Invariant Theory, Arxiv:1206.4774 , 2012 M.Audin, Torus Actions On Symplectic Manifolds, Birkhauser Progress in Mathematics,2004 R.Donagi, Group Law On The Intersection of Two Quadrics, Annali della Scuola NormaleSuperiore di Pisa - Classe di Scienze 7.2 ,1980, 217-239 R.Kottwiz, Stable trace formula: cuspidal tempered terms, Duke Math. J. 51 ,1984, no.3, 611–650. S.Chang, On the arithmetic of twists of superelliptic curves, Acta Arith 124 , 2006, 371–389 S.H. Weintraub, Guide To Advanced Linear Algebra, Mathematical Association of America Guides #6, 2011 S. Roman, Advanced Linear Algebra, Springer GTM 135, 2008 W.C.Waterhouse, Introduction to affine group schemes, Springer GTM 66, 1979 X.Wang, Pencils of quadrics and Jacobians of hyperelliptic curves, Harvard Ph.D. thesis.2013 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4715 | - |
| dc.description.abstract | 令 G 為一可簡約代數群、k 是一個特徵數為奇數的體、 ks 是 k 的分離封閉體,而 V 是 G 的一個表現。當我們 考慮 G(ks) 作用在 V (ks) 上的軌跡的時候,幾何不變量 理論給了我們一種分類這些軌跡的方法。然而當我們考 慮 G(k) 作用在 V (k) 上的軌跡時,我們對於這個問題並 沒有一個有系統的分類方法。在我的碩士論文裡,我研 讀了 Bhargava 跟 Gross 的論文,他們針對奇數維度特殊 正交群及它的一些表現發展了一套有系統的方法去分類 這些特殊情況的軌跡。Bhargava 與 Gross 首先把分類軌 跡的問題與伽羅瓦上同調理論做一個連結,而後利用這 個連結去發展一些新的觀點及方法分類這些特殊情況的 軌跡。 | zh_TW |
| dc.description.abstract | Let G be a reductive group , k be a field of odd characteris- tic with a seperable closure ks, and V be a representation of G. The geometric invariant theory deals with the classifica- tion of G(ks)-orbits on V . In this thesis, I study the paper of Bhargava and Gross that deals with the problem on the clas- sification of the G(k)-orbits on V which allows us to translate this problem into a language of Galois Cohomology. Then we deliver several approaches to solve this problem in some special cases. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-14T17:45:45Z (GMT). No. of bitstreams: 1 ntu-104-R02221005-1.pdf: 1963786 bytes, checksum: 4207d774f04f089391a46c7d5beaed93 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 1. Introduction 1
1.1. Relation between O_k and O_{k^s} 1 2. Setting 2 2.1. Orthogonal space 2 2.2. The special orthogonal group 4 2.3. Special representations of SO(W ) 4 2.4. A conventional use of notation 5 3. Main theorems 5 3.1. ThecaseV =W 5 3.2. TheV=Λ2(W)case 7 3.3. The V = Sym2(W ) case 12 4. more discussion on the representation V=Sym2(W) 15 4.1. The group scheme J[2] 15 4.2. Special classes in ker γ 18 5. Arithmetic fields 19 5.1. The finite field case 19 5.2. The non-archimedean local field case 21 5.3. Thek=Rcase 24 5.4. The Global field case 28 6. Appendix 29 6.1. Special case of Galois descent 29 References 31 | |
| dc.language.iso | en | |
| dc.subject | 算術不變量理論 | zh_TW |
| dc.subject | 特殊正交群 | zh_TW |
| dc.subject | 奇數維度 | zh_TW |
| dc.subject | Arithmetic Invariant Theory | en |
| dc.subject | SO_2n+1 | en |
| dc.title | 奇數維度特殊正交群的算術不變量理論 | zh_TW |
| dc.title | On Arithmetic Invariant Theory for Special Orthogonal Group of Odd Degree | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 李白飛(Pjek-Hwee Lee),謝銘倫(Ming-Lun Hsieh) | |
| dc.subject.keyword | 特殊正交群,奇數維度,算術不變量理論, | zh_TW |
| dc.subject.keyword | SO_2n+1,Arithmetic Invariant Theory, | en |
| dc.relation.page | 31 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2015-07-06 | |
| 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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