DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Hahn, Sang-Geun | - |
dc.contributor.advisor | 한상근 | - |
dc.contributor.author | Cheon, Jung-Hee | - |
dc.contributor.author | 천정희 | - |
dc.date.accessioned | 2011-12-14T04:38:34Z | - |
dc.date.available | 2011-12-14T04:38:34Z | - |
dc.date.issued | 1997 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=112602&flag=dissertation | - |
dc.identifier.uri | http://hdl.handle.net/10203/41791 | - |
dc.description | 학위논문(박사) - 한국과학기술원 : 수학과, 1997.2, [ [ii], 48 p. ] | - |
dc.description.abstract | In this thesis, we are concerned with the arithmetic of elliptic curves defined over a number field or a finite field. The main purpose of this thesis is on the orders of the reductions of a given point in the Mordell-Weil groups of elliptic curves. In Chapter 1, we introduce elliptic curves. To begin with, we explain some properties of the Mordell-Weil groups and present important theorems on elliptic curves defined over a number field. In addition, we define division polynomials of elliptic curves, which plays an important role in Chapter 2 and 3. In Chapter 2, we are concerned with supersingular elliptic curves. Let E be an elliptic curve defined over a finite field $F_p$ for a prime p≠2,3. Then we get the complete description of the $p^k$-th division polynomials for any positive integer k when E is supersingular. Also, we get a property of the division polynomials when E is ordinary. At last, we get a sufficient condition for ordinary primes. In Chapter 3, we prove the elliptic analogue of Bang``s theorem. Consider an elliptic curve E over a number field K. For any non-torsion point M∈E(K), the order of the reductions M mod p runs through all but finitely many positive integers as p runs through all good primes. Moreover, it runs through all positive integers for all but finitely many point M∈E(K). For singular primes, we estimate discrete valuations of division polynomials at each singular prime when evaluated at a point. | eng |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | 뱅의 정리 | - |
dc.subject | 수퍼싱귤러 | - |
dc.subject | 타원곡선 | - |
dc.subject | Division polynomial | - |
dc.subject | Bang``s theorem | - |
dc.subject | Supersingular | - |
dc.subject | Elliptic curve | - |
dc.subject | 분할다항식 | - |
dc.title | (The) orders of the reductions of a point in the mordell-weil group of an elliptic curve | - |
dc.title.alternative | 타원곡선의 모델-베일군에서 고정된 점의 줄임시 위수들 | - |
dc.type | Thesis(Ph.D) | - |
dc.identifier.CNRN | 112602/325007 | - |
dc.description.department | 한국과학기술원 : 수학과, | - |
dc.identifier.uid | 000935843 | - |
dc.contributor.localauthor | Hahn, Sang-Geun | - |
dc.contributor.localauthor | 한상근 | - |
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