메뉴 건너뛰기




Volumn 12, Issue 3, 2000, Pages 315-364

Large torsion subgroups of split Jacobians of curves of genus two or three

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0040211616     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.2000.008     Document Type: Article
Times cited : (111)

References (36)
  • 2
    • 84972562735 scopus 로고
    • The rank of elliptic curves
    • Brumer, A. and Kramer, K.: The rank of elliptic curves. Duke Math. J. 44 (1977), no. 4, 715-743
    • (1977) Duke Math. J. , vol.44 , Issue.4 , pp. 715-743
    • Brumer, A.1    Kramer, K.2
  • 3
    • 0001915970 scopus 로고
    • The Mordell-Weil group of curves of genus 2
    • M. Artin, J. Tate (eds.). Birkhäuser, Boston
    • Cassels, J. W. S.: The Mordell-Weil group of curves of genus 2. In: M. Artin, J. Tate (eds.). Arithmetic and Geometry I. Birkhäuser, Boston 1983, 27-60
    • (1983) Arithmetic and Geometry I , pp. 27-60
    • Cassels, J.W.S.1
  • 4
    • 84974050679 scopus 로고
    • The arithmetic of certain quartic curves
    • Cassels, J. W. S.: The arithmetic of certain quartic curves. Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), nos. 3-4, 201-218
    • (1985) Proc. Roy. Soc. Edinburgh Sect. A , vol.100 , Issue.3-4 , pp. 201-218
    • Cassels, J.W.S.1
  • 6
    • 0000133160 scopus 로고
    • Les schémas de modules de courbes elliptiques
    • A. Dold and B. Eckmann (eds.). Springer-Verlag, New York
    • Deligne, P. and Rapoport, M.: Les schémas de modules de courbes elliptiques. In: A. Dold and B. Eckmann (eds.). Modular Functions of One Variable II. Lecture Notes in Math. 349. Springer-Verlag, New York 1973, 143-316
    • (1973) Modular Functions of One Variable II. Lecture Notes in Math. , vol.349 , pp. 143-316
    • Deligne, P.1    Rapoport, M.2
  • 7
    • 0000804458 scopus 로고    scopus 로고
    • Exemples de courbes elliptiques de grand rang sur ℚ(t) et sur ℚ possédant des points d'ordre 2
    • Fermigier, S.: Exemples de courbes elliptiques de grand rang sur ℚ(t) et sur ℚ possédant des points d'ordre 2. C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), no. 10, 949-967
    • (1996) C. R. Acad. Sci. Paris Sér. I Math. , vol.322 , Issue.10 , pp. 949-967
    • Fermigier, S.1
  • 8
    • 38249017941 scopus 로고
    • Large rational torsion on abelian varieties
    • Flynn, E. V.: Large rational torsion on abelian varieties. J. Number Theory 36 (1990), no. 3, 257-265
    • (1990) J. Number Theory , vol.36 , Issue.3 , pp. 257-265
    • Flynn, E.V.1
  • 9
    • 0039703177 scopus 로고
    • Sequences of rational torsions on abelian varieties
    • Flynn, E. V.: Sequences of rational torsions on abelian varieties. Invent. Math. 106 (1991), no. 2, 433-442
    • (1991) Invent. Math. , vol.106 , Issue.2 , pp. 433-442
    • Flynn, E.V.1
  • 10
    • 0002177061 scopus 로고
    • On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2
    • J. Coates and S. T. Yau (eds.). International Press, Boston
    • Frey, G.: On elliptic curves with isomorphic torsion structures and corresponding curves of genus 2. In: J. Coates and S. T. Yau (eds.). Elliptic Curves, Modular Forms, and Fermat's Last Theorem. International Press, Boston 1995, 79-98
    • (1995) Elliptic Curves, Modular Forms, and Fermat's Last Theorem , pp. 79-98
    • Frey, G.1
  • 11
    • 0000316470 scopus 로고
    • Curves of genus 2 covering elliptic curves and an arithmetical application
    • G. van der Geer, F. Oort, and J. Steenbrink (eds.). Birkhäuser, Boston
    • Frey, G. and Kani, E.: Curves of genus 2 covering elliptic curves and an arithmetical application. In: G. van der Geer, F. Oort, and J. Steenbrink (eds.). Arithmetic Algebraic Geometry. Progress in Math. 89, Birkhäuser, Boston 1991, 153-176
    • (1991) Arithmetic Algebraic Geometry. Progress in Math. , vol.89 , pp. 153-176
    • Frey, G.1    Kani, E.2
  • 13
    • 0039827971 scopus 로고    scopus 로고
    • Constructing distinct curves with isomorphic Jacobians in characteristic zero
    • Howe, E. W.: Constructing distinct curves with isomorphic Jacobians in characteristic zero. Internat. Math. Res. Notices 1995, no. 4, 173-180
    • Internat. Math. Res. Notices , vol.1995 , Issue.4 , pp. 173-180
    • Howe, E.W.1
  • 14
    • 0041013661 scopus 로고    scopus 로고
    • Sous-groupes de torsion d'ordres élevés de Jacobiennes décomposable de courbes de genre 2
    • Howe, E. W., Leprévost. F., and Poonen, B.: Sous-groupes de torsion d'ordres élevés de Jacobiennes décomposable de courbes de genre 2. C. R. Acad. Sci. Paris Sér. I Math. 333 (1996), no. 9, 1031-1034
    • (1996) C. R. Acad. Sci. Paris Sér. I Math. , vol.333 , Issue.9 , pp. 1031-1034
    • Howe, E.W.1    Leprévost, F.2    Poonen, B.3
  • 15
    • 0031537202 scopus 로고    scopus 로고
    • The number of curves of genus two with elliptic differentials
    • Kani, E.: The number of curves of genus two with elliptic differentials. J. Reine Angew. Math. 485 (1997), 93-121
    • (1997) J. Reine Angew. Math. , vol.485 , pp. 93-121
    • Kani, E.1
  • 16
    • 0031139072 scopus 로고    scopus 로고
    • The existence of curves of genus two with elliptic differentials
    • Kani, E.: The existence of curves of genus two with elliptic differentials. J. Number Theory 64 (1997), no. 1, 130-161
    • (1997) J. Number Theory , vol.64 , Issue.1 , pp. 130-161
    • Kani, E.1
  • 17
    • 0000131981 scopus 로고
    • Arithmetic moduli of elliptic curves
    • Princeton University Press, Princeton
    • Katz, N. M. and Mazur, B.: Arithmetic Moduli of Elliptic Curves. Ann. of Math. Stud. 108. Princeton University Press, Princeton 1985
    • (1985) Ann. of Math. Stud. , vol.108
    • Katz, N.M.1    Mazur, B.2
  • 18
    • 84972529966 scopus 로고
    • Torsion points on elliptic curves defined over quadratic fields
    • Kenku, M. A. and Momose, F.: Torsion points on elliptic curves defined over quadratic fields. Nagoya Math. J. 109 (1988), 125-149
    • (1988) Nagoya Math. J. , vol.109 , pp. 125-149
    • Kenku, M.A.1    Momose, F.2
  • 19
    • 84959846941 scopus 로고
    • Universal bounds on the torsion of elliptic curves
    • Kubert, D.: Universal bounds on the torsion of elliptic curves. Proc. London Math. Soc. (3) 33 (1976), no. 2, 193-237
    • (1976) Proc. London Math. Soc. (3) , vol.33 , Issue.2 , pp. 193-237
    • Kubert, D.1
  • 20
    • 0010894735 scopus 로고
    • Curves of genus 2 with split Jacobian
    • Kuhn, R. M.: Curves of genus 2 with split Jacobian. Trans. Amer. Math. Soc. 307 (1988), no. 1, 41-49
    • (1988) Trans. Amer. Math. Soc. , vol.307 , Issue.1 , pp. 41-49
    • Kuhn, R.M.1
  • 21
    • 0037760150 scopus 로고
    • Famille de courbes de genre 2 munies d'une classe de diviseurs rationnels d'ordre 13
    • Leprévost F.: Famille de courbes de genre 2 munies d'une classe de diviseurs rationnels d'ordre 13. C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 7, 451-454
    • (1991) C. R. Acad. Sci. Paris Sér. I Math. , vol.313 , Issue.7 , pp. 451-454
    • Leprévost, F.1
  • 22
    • 25544443603 scopus 로고
    • Familles de courbes de genre 2 munies d'une classe de diviseurs rationnels d'ordre 15, 17, 19 ou 21
    • Leprévost, F.: Familles de courbes de genre 2 munies d'une classe de diviseurs rationnels d'ordre 15, 17, 19 ou 21. C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), no. 11, 771-774
    • (1991) C. R. Acad. Sci. Paris Sér. I Math. , vol.313 , Issue.11 , pp. 771-774
    • Leprévost, F.1
  • 23
    • 51249165077 scopus 로고
    • Torsion sur des familles de courbes de genre g
    • Leprévost, F.: Torsion sur des familles de courbes de genre g. Manuscripta Math. 75 (1992), no. 3, 303-326
    • (1992) Manuscripta Math. , vol.75 , Issue.3 , pp. 303-326
    • Leprévost, F.1
  • 25
    • 0040295097 scopus 로고
    • Points rationnels de torsion de jacobiennes de certaines courbes de genre 2
    • Leprévost, F.: Points rationnels de torsion de jacobiennes de certaines courbes de genre 2. C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 8, 819-821
    • (1993) C. R. Acad. Sci. Paris Sér. I Math. , vol.316 , Issue.8 , pp. 819-821
    • Leprévost, F.1
  • 26
    • 0010889775 scopus 로고
    • Jacobiennes de certaines courbes de genre 2 : Torsion et simplicité
    • Leprévost, F.: Jacobiennes de certaines courbes de genre 2 : torsion et simplicité. J. Théor. Nombres Bordeaux 7 (1995), no. 1, 283-306
    • (1995) J. Théor. Nombres Bordeaux , vol.7 , Issue.1 , pp. 283-306
    • Leprévost, F.1
  • 27
    • 0039111011 scopus 로고    scopus 로고
    • Sur une conjecture sur les points de torsion rationnels des jacobiennes de courbes
    • Leprévost, F.: Sur une conjecture sur les points de torsion rationnels des jacobiennes de courbes. J. Reine Angew. Math. 473 (1996), 59-68
    • (1996) J. Reine Angew. Math. , vol.473 , pp. 59-68
    • Leprévost, F.1
  • 28
    • 0039862056 scopus 로고    scopus 로고
    • Sur certains sous-groupes de torsion de jacobiennes de courbes hyper-elliptiques de genre g ≥ 1
    • Leprévost, F.: Sur certains sous-groupes de torsion de jacobiennes de courbes hyper-elliptiques de genre g ≥ 1. Manuscripta Math. 92 (1997), no. 1, 47-63
    • (1997) Manuscripta Math. , vol.92 , Issue.1 , pp. 47-63
    • Leprévost, F.1
  • 30
    • 51649164688 scopus 로고
    • Modular curves and the Eisenstein ideal
    • Mazur, B.: Modular curves and the Eisenstein ideal. Inst. Hautes Études Sci. Publ. Math. 47 (1977), 33-186 (1978)
    • (1977) Inst. Hautes Études Sci. Publ. Math. , vol.47 , pp. 33-186
    • Mazur, B.1
  • 31
    • 0001543668 scopus 로고
    • Formules explicites et minorations de conducteurs de variétés algébriques
    • Mestre, J.-F.: Formules explicites et minorations de conducteurs de variétés algébriques. Compositio Math. 58 (1986), no. 2, 209-232
    • (1986) Compositio Math. , vol.58 , Issue.2 , pp. 209-232
    • Mestre, J.-F.1
  • 32
    • 0002627221 scopus 로고
    • Abelian varieties
    • G. Cornell and J. H. Silverman (eds.). Springer-Verlag, New York
    • Milne, J.: Abelian varieties. In: G. Cornell and J. H. Silverman (eds.). Arithmetic Geometry. Springer-Verlag, New York 1986, 103-150
    • (1986) Arithmetic Geometry , pp. 103-150
    • Milne, J.1
  • 33
    • 0039110998 scopus 로고
    • Curves of genus 2 with a rational torsion divisor of order 23
    • Ogawa, H.: Curves of genus 2 with a rational torsion divisor of order 23. Proc. Japan Acad. Ser. A Math. Sci. 70 (1994), no. 9, 295-298
    • (1994) Proc. Japan Acad. Ser. A Math. Sci. , vol.70 , Issue.9 , pp. 295-298
    • Ogawa, H.1
  • 34
    • 0001459973 scopus 로고
    • Principally polarized abelian varieties of dimension two or three are Jacobian varieties
    • Oort, F. and Ueno, K.: Principally polarized abelian varieties of dimension two or three are Jacobian varieties. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 377-381
    • (1973) J. Fac. Sci. Univ. Tokyo Sect. IA Math. , vol.20 , pp. 377-381
    • Oort, F.1    Ueno, K.2
  • 35
    • 0000589747 scopus 로고
    • 2-descent on the Jacobians of hyperelliptic curves
    • Schaefer, E. F.: 2-descent on the Jacobians of hyperelliptic curves. J. Number Theory 51 (1995), no. 2, 219-232
    • (1995) J. Number Theory , vol.51 , Issue.2 , pp. 219-232
    • Schaefer, E.F.1
  • 36
    • 0003357475 scopus 로고
    • The arithmetic of elliptic curves
    • Springer-Verlag, New York
    • Silverman, J. H.: The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106. Springer-Verlag, New York, 1986
    • (1986) Grad. Texts in Math. , vol.106
    • Silverman, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.