Duke Mathematical Journal

Cycles in a product of elliptic curves, and a group analogous to the class group

Stephen J. M. Mildenhall
Source: Duke Math. J. Volume 67, Number 2 (1992), 387-406.
First Page: Show Hide
Primary Subjects: 14C25
Secondary Subjects: 11G40, 11G45, 14C35, 14J20
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077294409
Mathematical Reviews number (MathSciNet): MR1177312
Zentralblatt MATH identifier: 0788.14004
Digital Object Identifier: doi:10.1215/S0012-7094-92-06715-9

References

[Bl] S. Bloch, Algebraic $K$-theory, motives and algebraic cycles, to appear in Proceedings of 1990 ICM.
Mathematical Reviews (MathSciNet): MR2571504
[BlKa] S. Bloch and K. Kato, $L$-functions and Tamagawa numbers of motives, The Grothendieck Festschrift, Vol. I ed. P. Cartier, et al., Progr. Math., vol. 86, Birkhäuser Boston, Boston, MA, 1990, pp. 333–400.
Mathematical Reviews (MathSciNet): MR92g:11063
Zentralblatt MATH: 0768.14001
[BLR] S. Bosch, W. Lütkebohmert, and M. Raynaud, Néron models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 21, Springer-Verlag, Berlin, 1990.
Mathematical Reviews (MathSciNet): MR91i:14034
Zentralblatt MATH: 0705.14001
[Co] P. M. Cohn, Algebra. Vol. 2, John Wiley & Sons, London-New York-Sydney, 1977.
Mathematical Reviews (MathSciNet): MR58:26625
Zentralblatt MATH: 0341.00002
[CTR] J.-L. Colliot-Thélène and W. Raskind, Groupe de Chow de codimension deux des variétés définies sur un corps de nombres: un théorème de finitude pour la torsion, Invent. Math. 105 (1991), no. 2, 221–245.
Mathematical Reviews (MathSciNet): MR92j:14009
Zentralblatt MATH: 0752.14004
Digital Object Identifier: doi:10.1007/BF01232266
[CTS] J.-L. Colliot-Thélène and J.-J. Sansuc, On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch, Duke Math. J. 48 (1981), no. 2, 421–447.
Mathematical Reviews (MathSciNet): MR83e:14007
Zentralblatt MATH: 0479.14006
Digital Object Identifier: doi:10.1215/S0012-7094-81-04824-9
Project Euclid: euclid.dmj/1077314658
[DR] P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1973, 143–316. Lecture Notes in Math., Vol. 349.
Mathematical Reviews (MathSciNet): MR49:2762
Zentralblatt MATH: 0281.14010
[D] D. R. Dorman, Global orders in definite quaternion algebras as endomorphism rings for reduced CM elliptic curves, Théorie des nombres (Quebec, PQ, 1987) eds. J.-M. de Koninck, C. Levesque, and W. de Gruyter, de Gruyter, Berlin, 1989, pp. 108–116.
Mathematical Reviews (MathSciNet): MR90j:11043
Zentralblatt MATH: 0697.12011
[F] W. Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984.
Mathematical Reviews (MathSciNet): MR85k:14004
Zentralblatt MATH: 0541.14005
[I] T. Ibukiyama, On maximal orders of division quaternion algebras over the rational number field with certain optimal embeddings, Nagoya Math. J. 88 (1982), 181–195.
Mathematical Reviews (MathSciNet): MR85c:11112
Zentralblatt MATH: 0473.12012
Project Euclid: euclid.nmj/1118787011
[KS] Kazuya Kato and Shuji Saito, Global class field theory of arithmetic schemes, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983), Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 255–331.
Mathematical Reviews (MathSciNet): MR88c:11041
Zentralblatt MATH: 0614.14001
[KM] N. M. Katz and B. Mazur, Arithmetic moduli of elliptic curves, Annals of Mathematics Studies, vol. 108, Princeton University Press, Princeton, NJ, 1985.
Mathematical Reviews (MathSciNet): MR86i:11024
Zentralblatt MATH: 0576.14026
[Lg1] S. Lang, Introduction to Arakelov theory, Springer-Verlag, New York, 1988.
Mathematical Reviews (MathSciNet): MR89m:11059
Zentralblatt MATH: 0667.14001
[Lg2] S. Lang, Elliptic functions, 2nd edition ed., Graduate Texts in Mathematics, vol. 112, Springer-Verlag, New York, 1987.
Mathematical Reviews (MathSciNet): MR88c:11028
Zentralblatt MATH: 0615.14018
[Mz1] B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. (1977), no. 47, 33–186 (1978).
Mathematical Reviews (MathSciNet): MR80c:14015
Zentralblatt MATH: 0394.14008
Digital Object Identifier: doi:10.1007/BF02684339
[M] S. J. M. Mildenhall, Cycles in a Product of Curves, thesis, Univ. of Chicago.
[Mi] J. S. Milne, Jacobian varieties, Arithmetic geometry (Storrs, Conn., 1984), Springer, New York, 1986, pp. 167–212.
Mathematical Reviews (MathSciNet): MR861976
Zentralblatt MATH: 0604.14018
[Ogg1] A. P. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449–462.
Mathematical Reviews (MathSciNet): MR51:514
Zentralblatt MATH: 0314.10018
[Ogg2] A. P. Ogg, Rational points on certain elliptic modular curves, Analytic number theory (Proc. Sympos. Pure Math., Vol XXIV, St. Louis Univ., St. Louis, Mo., 1972), Amer. Math. Soc., Providence, R.I., 1973, pp. 221–231.
Mathematical Reviews (MathSciNet): MR49:2743
Zentralblatt MATH: 0273.14008
[Ogg3] A. P. Ogg, Modular functions, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 521–532.
Mathematical Reviews (MathSciNet): MR82h:10037
Zentralblatt MATH: 0448.10021
[Ram] D. Ramakrishnan, Regulators, algebraic cycles, and values of $L$-functions, Algebraic $K$-theory and algebraic number theory (Honolulu, HI, 1987), Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 183–310.
Mathematical Reviews (MathSciNet): MR90e:11094
Zentralblatt MATH: 0694.14002
[Ra1] W. Raskind, Algebraic $K$-theory, étale cohomology and torsion algebraic cycles, Algebraic $K$-theory and algebraic number theory (Honolulu, HI, 1987), Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 311–341.
Mathematical Reviews (MathSciNet): MR90d:14011
Zentralblatt MATH: 0669.14002
[Ra2] W. Raskind, Torsion algebraic cycles on varieties over local fields, Algebraic $K$-theory: connections with geometry and topology (Lake Louise, AB, 1987) eds. J. F. Jardine and V. P. Snaith, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 279, Kluwer Acad. Publ., Dordrecht, 1989, pp. 343–388.
Mathematical Reviews (MathSciNet): MR91f:14007
Zentralblatt MATH: 0709.14005
[Sal] P. Salberger, Zero-cycles on rational surfaces over number fields, Invent. Math. 91 (1988), no. 3, 505–524.
Mathematical Reviews (MathSciNet): MR89c:14010
Zentralblatt MATH: 0688.14008
Digital Object Identifier: doi:10.1007/BF01388784
[Sil] J. H. Silverman, The arithmetic of elliptic curves, Graduate Texts in Mathematics, vol. 106, Springer-Verlag, New York, 1986.
Mathematical Reviews (MathSciNet): MR87g:11070
Zentralblatt MATH: 0585.14026
[Wat] W. C. Waterhouse, Abelian varieties over finite fields, Ann. Sci. École Norm. Sup. (4) 2 (1969), 521–560.
Mathematical Reviews (MathSciNet): MR42:279
Zentralblatt MATH: 0188.53001

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?