Skip to main content
Log in

On thep-adic height of Heegner cycles

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Atkin, A.O.L., Lehner, J.: Hecke operators onΓ 0(m), Math. Ann.185, 134–160 (1970)

    Google Scholar 

  2. Atkin, A.O.L., Li, W.: Twists of Newforms and Pseudo-Eigenvalues ofW-Operators, Invent. Math.48, 221–243 (1978)

    Google Scholar 

  3. Beilinson, A.A.: Height pairing between algebraic cycles, in:K-theory, Arithmetic and Geometry; Seminar, Moscow 1984–86 (Manin, Yu.I., ed.), Lect. Notes in Math.1289, Springer, Berlin, Heidelberg, New York, 1987, pp. 1–26

    Google Scholar 

  4. Berthelot, P.: Remarks on Faltings' approach to theC cris conjecture, preprint Rennes, June 21, 1994

  5. Bloch, S., Kato, K.:L-functions and Tamagawa numbers of motives, in: The Grothendieck Festschrift I. Progress in Mathematics86, Birkhäuser, Boston, Basel, Berlin, 1990, pp. 333–400

    Google Scholar 

  6. Brylinski, J.-L.: Heights for local systems on curves, Duke Math. J.59, 1–26 (1989)

    Google Scholar 

  7. Bump, D., Friedberg, S., Hoffstein, J.: Nonvanishing theorems forL-functions of modular forms and their derivatives, Invent. Math.102, 543–618 (1990)

    Google Scholar 

  8. Carayol, H.: Sur les représentationsl-adiques, attachées aux formes modulaires de Hilbert, Ann. Sci. Ec. Norm. Supér.19, 409–469 (1986)

    Google Scholar 

  9. Deligne, P.: Formes modulaires et représentations ℓ-adiques, in: Séminaire Bourbaki, No 355, Lect. Notes in Math,179, Springer, Berlin, Heidelberg, New York, 1971, pp. 139–172

    Google Scholar 

  10. Deligne, P.: La conjecture de Weil II, Publ. Math. de l'I.H.E.S.52, 137–252 (1980)

    Google Scholar 

  11. Faltings, G.: Crystalline cohomology andp-adic Galois representations, in: Algebraic Analysis, Geometry, and Number Theory (Igusa, J.-I., ed.), John Hopkins University Press, Baltimore, 1990, pp. 25–79

    Google Scholar 

  12. Fontaine, J.-M., Messing, W.:p-adic periods andp-adic étale cohomology, in: Current Trends in Arithmetic Algebraic Geometry. Contemporary Mathematics67, American Mathematical Society, Providence, Rhode Island, 1987, pp. 179–207

    Google Scholar 

  13. Fontaine, J.-M., Perrin-Riou, B.: Autour des conjectures de Bloch et Kato: cohomologie galoisienne et valeurs de fonctions L, in: Motives, Proceedings of AMS Summer Research Conference held in July 1991, Seattle, Proceedings of Symposia in Pure Mathematics55/I, American Mathematical Society, Providence, Rhode Island, 1994, pp. 599–706

    Google Scholar 

  14. Greenberg, R.: Iwasawa Theory forp-adic Representations, in: Algebraic Number Theory, in honor of K. Iwasawa, Advanced Studies in Pure Mathematics, Academic Press, Boston, 1989, pp. 97–137

    Google Scholar 

  15. Gros, M.: Régulateurs syntomiques et valeurs de fonctionsL p-adiques I, Invent. Math.99, 293–320 (1990)

    Google Scholar 

  16. Gross, B.H.: Heegner points onX 0(N), in: Modular Forms (Rankin, R.A., ed.), Ellis Horwood, Chichester, 1984, pp. 87–106

    Google Scholar 

  17. Gross, B.H., Zagier, D.B.: Heegner points and derivatives ofL-series, Invent. Math.84, 225–320 (1986)

    Google Scholar 

  18. Gross, B.H., Kohnen, W., Zagier, D.B.: Heegner points and derivatives ofL-series II, Math. Ann.278, 497–562 (1987)

    Google Scholar 

  19. Hatcher, R.L.: Heights andL-series, Canad. J. Math.XLII, 533–560 (1990)

    Google Scholar 

  20. Hida, H.: Ap-adic measure attached to the zeta functions associated with two elliptic modular forms. I, Invent. Math.79, 159–195 (1985)

    Google Scholar 

  21. Hida, H.: Ap-adic measure attached to the zeta functions associated with two elliptic modular forms. II, Ann. Inst. Fourier38, 1–83 (1988)

    Google Scholar 

  22. Iwaniec, H.: On the order of vanishing of modularL-functions at the critical point, Séminaire de Théorie des Nombres, Bordeaux2, 365–376 (1990)

    Google Scholar 

  23. Jannsen, U.: Continuous Étale Cohomology, Math. Ann.280, 207–245 (1988)

    Google Scholar 

  24. Jannsen, U.: Mixed Motives and AlgebraicK-Theory, Lect. Notes in Math.1400, Springer, Berlin, Heidelberg, New York, 1990

    Google Scholar 

  25. Kato, K., Messing, W.: syntomic cohomology andp-adic étale cohomology, Tôhoku Math. J.44, 1–9 (1992)

    Google Scholar 

  26. Katz, N., Mazur, B.: Arithmetic moduli of elliptic curves, Ann. of Math. Studies108, Princeton Univ. Press, Princeton, 1985

    Google Scholar 

  27. Katz, N., Messing, W.: Some consequences of the Riemann hypothesis for varieties over finite fields, Invent. Math.,23, 73–77 (1974)

    Google Scholar 

  28. Kolyvagin, V.A.: Euler systems, in: The Grothendieck Festschrift II, Progress in Mathematics87, Birkhäuser, Boston, Basel, Berlin, 1990, pp. 435–483

    Google Scholar 

  29. Lingen, J. van der: Intersection of Heegner divisors onX 0(N), Minor Thesis, Amsterdam University

  30. Mazur, B., Tate, J., Teitelbaum, J.: Onp-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math.84, 1–48 (1986)

    Google Scholar 

  31. Murty, V.K., Murty, M.R.: Mean values of derivatives of modularL-series, Ann. of Math.133, 447–475 (1991)

    Google Scholar 

  32. Nekovář, J.: Kolyvagin's method for Chow groups of Kuga-Sato varieties, Invent. Math.107, 99–125 (1992)

    Google Scholar 

  33. Nekovář, J.: Onp-adic height pairings, in: Séminaire de théorie des nombres de Paris 1990/91, Progress in Math.108, (David, S., ed.), Birkhäuser, Boston, 1993, pp. 127–202

    Google Scholar 

  34. Nekovář, J.: Syntomic cohomology andp-adic regulators, in preparation

  35. Perrin-Riou, B.: FonctionsL p-adiques associées à une forme modulaire et à un corps quadratique imaginaire, J. London Math. Soc.38, 1–32 (1988)

    Google Scholar 

  36. Perrin-Riou, B.: Points de Heegner et dérivées de fonctionsL p-adiques, Invent. Math.89, 455–510 (1987)

    Google Scholar 

  37. Perrin-Riou, B: Théorie d'Iwasawa et hauteursp-adiques, Invent. Math.109 (1992), 137–185

    Google Scholar 

  38. Scholl, A.J.: Motives for modular forms, Invent. Math.100, 419–430 (1990)

    Google Scholar 

  39. Scholl, A.J.: Height pairings and values ofL-functions, in: Motives, Proceedings of AMS Summer Research Conference held in July 1991, Seattle, Proceedings of Symposia in Pure Mathematics55/I, American Mathematical Society, Providence, Rhode Island, 1994, pp. 571–598

    Google Scholar 

  40. Schoen, C.: Complex multiplication cycles and a conjecture of Beilinson and Bloch, Trans. A.M.S.339 (1993), 87–115

    Google Scholar 

  41. Schneider, P.:p-adic height pairings I, Invent. Math.69, 401–409 (1982)

    Google Scholar 

  42. Schneider, P.:p-adic height pairings II, Invent. Math.79, 329–374 (1985)

    Google Scholar 

  43. Serre, J.-P.: Cohomologie Galoisienne, Lect. Notes in Math.5, Springer, Berlin, Göttingen, Heidelberg, New York, 1964

    Google Scholar 

  44. Serre, J.-P., Tate, J.: Good reduction of abelian varieties, Ann. of Math.88, 492–517 (1968)

    Google Scholar 

  45. Shimura, G.: The Special Values of the Zeta Functions Associated with Cusp Forms, Comm. Pure Appl. Math.39, 783–804 (1976)

    Google Scholar 

  46. Siegel, C.L.: Advanced Analytic Number Theory, Tata Institute for Fundamental Research, Bombay, 1980

    Google Scholar 

  47. Skoruppa, N.-P., Zagier, D.B.: Jacobi forms and a certain space of modular forms, Invent. Math.94, 113–146 (1988)

    Google Scholar 

  48. Sturm, J.: Projections ofC automorphic forms, Bull. AMS2, 435–439 (1980)

    Google Scholar 

  49. Tate, J.: Relations betweenK 2 and Galois cohomology, Invent. Math.36, 257–274 (1976)

    Google Scholar 

  50. Waldspurger, J.-L.: Correspondences de Shimura, in: Proc. ICM 1983 Warszawa, pp. 525–531

  51. Wiles, A.: On ordinary λ-adic representations associated to modular forms, Invent. Math.94, 529–573 (1988)

    Google Scholar 

  52. Cohomologie Étale, Lect. Notes in Math.569, Springer, Berlin, Heidelberg, New York, 1977

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nekovář, J. On thep-adic height of Heegner cycles. Math. Ann. 302, 609–686 (1995). https://doi.org/10.1007/BF01444511

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01444511

Navigation