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On some conjectures on the arithmetic of elliptic curves : 타원 곡선의 수론에 관한 몇 가지 가설들
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 변동호 | - |
dc.contributor.author | 김태경 | - |
dc.date.accessioned | 2017-07-14T00:42:22Z | - |
dc.date.available | 2017-07-14T00:42:22Z | - |
dc.date.issued | 2016-02 | - |
dc.identifier.other | 000000133283 | - |
dc.identifier.uri | https://hdl.handle.net/10371/121310 | - |
dc.description | 학위논문 (박사)-- 서울대학교 대학원 : 수리과학부, 2016. 2. 변동호. | - |
dc.description.abstract | The goal of the present thesis is twofold | - |
dc.description.abstract | we show the two conjectures concerning the arithmetic of elliptic curves: the Stein–Watkins conjecture (for 5-isogenies) and the Gross--Zagier conjecture.
Essentially, Stein--Watkins conjecture tells us about the relations of optimal curves in given rational isogeny class of elliptic curves. In this thesis we show the two optimal curves differ by a 5-isogeny if and only if the isogeny class is '11a'. The Gross--Zagier conjecture provides a theoretical evidence to the strong form of Birch and Swinnerton-Dyer conjecture. We show when elliptic curves have particular types of rational torsion subgroups, the order of the torsion subgroup divides certain arithmetic invariants attached to the curve. | - |
dc.description.tableofcontents | Chapter 1. Introduction 1
Chapter 2. Elliptic curves 5 Chapter 3. Differing isogenies of optimal curves 45 Chapter 4. GrossZagier conjecture 59 Bibliography 127 Abstract (in Korean) 135 | - |
dc.format | application/pdf | - |
dc.format.extent | 3564039 bytes | - |
dc.format.medium | application/pdf | - |
dc.language.iso | en | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | elliptic curves | - |
dc.subject | Birch and Swinnerton-Dyer conjecture | - |
dc.subject | Gross--Zagier theorem | - |
dc.subject | isogeny of elliptic curves | - |
dc.subject.ddc | 510 | - |
dc.title | On some conjectures on the arithmetic of elliptic curves | - |
dc.title.alternative | 타원 곡선의 수론에 관한 몇 가지 가설들 | - |
dc.type | Thesis | - |
dc.contributor.AlternativeAuthor | Taekyung Kim | - |
dc.description.degree | Doctor | - |
dc.citation.pages | xiv, 137 | - |
dc.contributor.affiliation | 자연과학대학 수리과학부 | - |
dc.date.awarded | 2016-02 | - |
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