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Minimal Models of Rational Elliptic Curves with Non-trivial Torsion
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Minimal Models of Rational Elliptic Curves with Non-trivial Torsion. |
| 개인저자 | Barrios, Alexander J. |
| 단체저자명 | Purdue University. Mathematics. |
| 발행사항 | [S.l.]: Purdue University., 2018. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2018. |
| 형태사항 | 372 p. |
| 기본자료 저록 | Dissertation Abstracts International 79-10B(E). Dissertation Abstract International |
| ISBN | 9780438010307 |
| 학위논문주기 | Thesis (Ph.D.)--Purdue University, 2018. |
| 일반주기 |
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Adviser: Edray H. Goins. |
| 요약 | This dissertation concerns the formulation of an explicit modified Szpirobconjecture and the classification of minimal discriminants of rational elliptic curves with non-trivial torsion subgroup. |
| 요약 | The Frey curve y2=x( x+a) ( x-b) is a two-parameter family of elliptic curves which comes equipped with an easily computable minimal discriminant which helped pave the mathematical bridge that led to the proof of Fermat's Last Theorem. In this |
| 요약 | The second theme of this dissertation concerns the modified Szpiro conjecture, which is equivalent to the ABC Conjecture. Roughly speaking, the modified Szpiro conjecture states that certain elliptic curves, known as good elliptic curves, are ra |
| 요약 | Lastly, we use the classification of minimal discriminants to study the local data of rational elliptic curves at a given prime via Tate's Algorithm. These results and a study of the naive height of an elliptic curve allow us to prove that there |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
