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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2009.1
- 수록면
- 419 - 424 (6page)
이용수
초록· 키워드
오류제보하기
Let J be the Jacobian variety of a hyperelliptic curve over Q. Let M be the
field generated by all square roots of rational integers over a finite number field K. Then we prove that the Mordell-Weil group J(M) is the direct sum of a finite torsion group and a free Z-module of infinite rank. In particular, J(M) is not a divisible group. On the other hand, if fM is an extension of M which contains all the torsion points of J over Q, then [수식] is a divisible group of infinite rank, where fMsol is the maximal solvable extension of fM.
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등록된 정보가 없습니다.
참고문헌 (8)
참고문헌 신청
G. Faltings / 1983 / Endlichkeitss¨atze f¨ur abelsche Variet¨aten ¨uber Zahlk¨orpern / Invent. Math 73 (3) : 349 ~ 366
G. Faltings / 1984 / Erratum: ”Finiteness theorems for abelian varieties over number fields / Invent. Math 75 (2) : 381 ~
G. Frey / 1974 / Approximation theory and the rank of abelian varieties over large algebraic fields / Proc. London Math. Soc 28 : 112 ~ 128
H. Imai / 1980 / On the rational points of some Jacobian varieties over large algebraic number fields / Kodai Math. J 3 : 56 ~ 58
J. Top / 1988 / A remark on the rank of Jacobians of hyperelliptic curves over Q over certain elementary Abelian 2-extension / Tohoku Math. J 40 : 613 ~ 616
G. Faltings / 1984 / Erratum: ”Finiteness theorems for abelian varieties over number fields / Invent. Math 75 (2) : 381 ~
G. Frey / 1974 / Approximation theory and the rank of abelian varieties over large algebraic fields / Proc. London Math. Soc 28 : 112 ~ 128
H. Imai / 1980 / On the rational points of some Jacobian varieties over large algebraic number fields / Kodai Math. J 3 : 56 ~ 58
J. Top / 1988 / A remark on the rank of Jacobians of hyperelliptic curves over Q over certain elementary Abelian 2-extension / Tohoku Math. J 40 : 613 ~ 616
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