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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠(Ki-Seng Tan) | |
| dc.contributor.author | Chia-Chen Wang | en |
| dc.contributor.author | 王家成 | zh_TW |
| dc.date.accessioned | 2021-05-14T17:44:00Z | - |
| dc.date.available | 2015-08-11 | |
| dc.date.available | 2021-05-14T17:44:00Z | - |
| dc.date.copyright | 2015-08-11 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-08-03 | |
| dc.identifier.citation | [1] Mazur B.,Rubin K.:Ranks of twists of elliptic curves and Hilbert's tenth problem. Invent. Math. 181
(2010), 541-575. [2] Silverman J.H.: The Arithmetic of Elliptic Curves, Springer GTM 106, 1986 [3] Silverman J.H.: Advanced Topics in the Arithmetic of Elliptic Curves, Springer GTM 151, 1994 [4] Lang S.: Algebraic groups over finite fields. Amer.J.Math.78(1956),555-563 [5] Kramer,K.:Arithmetic of elliptic curves upon quadratic extension, Trans.Am.Math.Soc,264, 121- 135(1981) [6] Tate, J.:Duality theorems in Galois cohomology over number fields. In: Proc. Intern. Congr. Math., Stockholm, pp.234-241(1962) [7] Cassels, J.W.S.: Arithmetic on curves of genus 1. VII. On conjectures of Birch and Swinnerton-Dyer. J. Reine Angew. Math. 217, 180-199(1965) [8] Rubin, K.: Euler Systems. Annals of Math. Studies, vol. 147. Princeton University Press, Princetion (2000) [9] Milne, J.S.: Class Field Theory (v4.02). 2013, Available at www.jmilne.org/math/ [10] Milne, J.S.: Arithmetic Duality Theorems. Perspectives in Math., vol. 1. Academic Press, San Diego (1986) | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4605 | - |
| dc.description.abstract | For an elliptic curve, we care about the Mordell-Weil group on it. Espically we care about the rank of this group. On the other hand, it is known that the F2-dimension of Selmer group of an elliptic curve is an finite upper bound of the rank of the Mordell-Weil group.
In this thesis, we study the result of Mazur and Rubin. They view the Selmer group and the twisted Selmer group as contained in the same set. Analyzing the local Selmer group, which tells us when will them be the same or intersect to zero. By this we can see the relation between the dimension of Selmer group and that of twisted Selmer group. Then we know that under some conditions, elliptic curve have abitrary twisted Selmer rank. IV | en |
| dc.description.provenance | Made available in DSpace on 2021-05-14T17:44:00Z (GMT). No. of bitstreams: 1 ntu-104-R02221027-1.pdf: 383015 bytes, checksum: f5fc34141a61b889093c1e53b9676039 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 口試委員會審定書I
誌謝II 摘要III Abstract IV 1. Introduction 1 2. Settings and basic facts 2 2.1. Settings 3 2.2. Selmer groups 3 2.3. The quadratic twists 5 2.4. The structure of E(Kv) 6 2.5. Local Tate duality 9 3. Local results 9 3.1. The size of H1f (Kv;E[2]) 10 3.2. Relations involving E and EF 12 3.3. The unramified case 13 3.4. Summary 15 4. Global results 16 4.1. The parity of d2(E/K) 17 4.2. Comparing Selmer groups 20 4.3. Special results on Galois groups 23 5. Twisting to lower and raise the Selmer rank 26 5.1. The proof of Theorem 1 27 5.2. The proof of Theorems 2 30 References 32 | |
| dc.language.iso | zh-TW | |
| dc.title | 探討橢圓曲線經扭變後之秩 | zh_TW |
| dc.title | On rank of twists of elliptic curves | 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 | 橢圓曲線,秩,賽爾曼群,扭變, | zh_TW |
| dc.subject.keyword | elliptic curve,rank,Mordel-Weil group,Selmer group,twist, | en |
| dc.relation.page | 32 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2015-08-03 | |
| 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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