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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/7759完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Shen tan) | |
| dc.contributor.author | Chun-Wei Lee | en |
| dc.contributor.author | 李俊緯 | zh_TW |
| dc.date.accessioned | 2021-05-19T17:52:36Z | - |
| dc.date.available | 2022-08-20 | |
| dc.date.available | 2021-05-19T17:52:36Z | - |
| dc.date.copyright | 2017-08-20 | |
| dc.date.issued | 2017 | |
| dc.date.submitted | 2017-07-25 | |
| dc.identifier.citation | [1] J. Cassels and A. F. eds. Algebraic Number Theory. Academic Press, 1967.
[2] F. D. Y. Diaz. Tables minorant la racine n-ième du discriminant d’un corps de degré n. Publications mathématiques d’Orsay, 1980. [3] J. M. Fontaine. Il n’y a pas de variété abélienne sur Z. Inventiones mathematicæ, pages 515–538, 1985. [4] A. Grothendieck. Éléments de géométrie algébrique: IV.Étude locale des schémas et des morphismes de schémas. Publications mathématiques de l’I.H.É.S., 1964. [5] R. Hartshorne. Algebraix Geometry. Springer-Verlag, 1977. [6] J. Milne. Étale Cohomology. Princeton University Press, 1980. [7] J. Milne. Abelian varieties. In G. Cornell and J. H. Silverman, editors, Arithmetic Geometry, chapter 5, pages 103–150. Springer-Verlag, 1986. [8] D. Mumford. Abelian Varieties. Oxford University Press, 1985. [9] M. Raynaud. Passage au quotient par une relation d’équivalence plate. In T.A.Springer, editor, Proceedings of a Conference on Local Fields, pages 78–85. Springer-Verlag, 1966. [10] M. Raynaud. Schémas en groupes de type (p,...,p). Bulletin de la S.M.F., pages 241–280, 1974. [11] J. P. Serre. Local Fields. Springer-Verlag, 1979. [12] L. C. Washington. Introduction to Cyclotomic Fields. Springer-Verlag, 1980. [13] W. C. Waterhouse. Introduction to affine group schemes. Springer-Verlag, 1979. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/7759 | - |
| dc.description.abstract | 阿貝爾簇是一個有阿貝爾群結構的簇。這些簇是在多個數學領域裡有特別重要性的幾何物件。我們對於有理數上的阿貝爾簇在不同質數下的化約感興趣。特別的，我們想知道是否一個阿貝爾簇的化約仍然是阿貝爾簇。我們知道一個阿貝爾簇只會在有限個質數上的化約不是阿貝爾簇。不過一個阿貝爾簇不會在所有質數上的化約都是阿貝爾簇。
這是Fontaine的定理。但Fontaine的證明對於初學者來說並不容易，所以我展開證明中的細節，讓潛在的讀者更能了解。 | zh_TW |
| dc.description.abstract | A variety is called an abelian variety if it has an abelian group structure. These varieties are special geometric objects of particular importance in multiple mathematics fields. We are concerned with the reductions of abelian varieties over the field of rational numbers modulo different primes. In particular, we are interested in whether the reduction of an abelian variety remains an abelian variety.
It is well-known for years that the reduction is still an abelian variety, except for finitely many primes. However, it cannot be an abelian variety modulo every prime. This is a theorem of Fontaine. But Fontaine's proof is not easy for beginners. So I expound the details of the proof to make it easier for potential readers. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-19T17:52:36Z (GMT). No. of bitstreams: 1 ntu-106-R04221016-1.pdf: 544976 bytes, checksum: e95dce6b1cfb03c6d355b0ac265d6c7c (MD5) Previous issue date: 2017 | en |
| dc.description.tableofcontents | 誌謝 iii
Acknowledgements v 摘要 vii Abstract ix Introduction 1 The main result 1 Notation 4 Group schemes 4 Examples 5 The Cartier duality and Deligne’s theorem 6 Étale group schemes 10 Local group schemes 12 Fontaine’s bound and its consequences 15 The ramification theory 16 Divided power sturctures 21 The relative differential forms 24 The proof 28 The choice of a prime 32 The global ramification theory 33 The decomposition theorem 38 Appendices 45 Rank 2 groups 45 An increasing function 46 Bibliography 49 | |
| dc.language.iso | en | |
| dc.title | 無全域良化約之阿貝爾簇 | zh_TW |
| dc.title | There are no abelian schemes over Z | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 105-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 謝銘倫(Ming-Lun Hsieh),紀文鎮(Wen-Chen Chi) | |
| dc.subject.keyword | 阿貝爾簇,良化約,Fontaine 上界,Neron 模型,分冪理想, | zh_TW |
| dc.subject.keyword | Abelian varieties,Good reduction,Fontaine bound,Neron model,Divided power ideals, | en |
| dc.relation.page | 49 | |
| dc.identifier.doi | 10.6342/NTU201701790 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2017-07-25 | |
| 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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