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Kolyvagin's method for Chow groups of Kuga-Sato varieties

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References

  1. Atkin, A.O.L., Lehner, J.: Hecke operators on Γ0(m). Math. Ann.185, 135–160 (1970)

    Google Scholar 

  2. Bloch, S., Kato, K.:L-functions and Tamagawa numbers of motives. In: The Grothendieck Festschrift, vol. I. (Prog. Math., vol. 86, pp. 333–400) Boston Basel Berlin: Birkhäuser 1990

    Google Scholar 

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

    Google Scholar 

  4. Carayol, H.: Sur les représentationsl-adiques attachées aux formes modulaires de Hilbert. Ann. Sci. Éc. Norm. Supér.19, 409–468 (1986)

    Google Scholar 

  5. Deligne, P.: Formes modulaires et représentationsl-adiques; Séminaire Bourbaki 1968/69 exp. 355. (Lect. Notes Math., vol. 179, pp. 139–172) Berlin Heidelberg New York: Springer 1971

    Google Scholar 

  6. Faltings, G.: Crystalline cohomology andp-adic Galois representations. In: Proceedings 1st JAMI-conference, pp. 25–79. Baltimore: John Hopkins University Press 1990

    Google Scholar 

  7. Flach, M.: A generalization of the Cassels-Tate pairing. J. Reine Angew. Math.412, 113–127 (1990)

    Google Scholar 

  8. Greenberg, R.: Iwasawa Theory forp-adic Representations. In: Algebraic Number Theory (in honor of K. Iwasawa). (Adv. Stud. Pure Math., vol. 17, pp. 97–137) Academic Press 1989

  9. Gross, B.: Kolyvagin's work on modular elliptic curves. In: Coates, J., Taylor, M.J. (eds.)L-functions and Arithmetic. Proceedings, Durham 1989. (Lond. Math. Soc. Lect. Note Ser., vol. 153, pp. 235–256) Cambridge: Cambridge University Press 1991

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. Jannsen, U.: Mixed Motives and Algebraic K-Theory. (Lect. Notes Math., vol. 1400) Berlin Heidelberg New York: Springer 1990

    Google Scholar 

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

    Google Scholar 

  14. Kolyvagin, V.A.: Finiteness ofE(Q) andIII(E,Q) for a subclass of Weil curves. Izv. Akad. Nauk SSSR, Ser. Mat.52, No. 3, 522–540 (1988)

    Google Scholar 

  15. Kolyvagin, V.A.: On Mordell-Weil and Šafarevič-Tate groups for Weil elliptic curves. Izv. Akad. Nauk SSSR, Ser. Mat.52, No. 6, 1154–1180 (1988)

    Google Scholar 

  16. Kolyvagin, V.A.: Euler systems. In: The Grothendieck Festschrift, vol. II. (Prog. Math., vol. 87, pp. 435–483) Boston Basel Berlin: Birkhäuser 1990

    Google Scholar 

  17. Kolyvagin, V.A.: On the structure of Šafarevič-Tate groups. (Preprint 1990)

  18. Milne, J.S.: Étale cohomology. Princeton: Princeton University Press 1980

    Google Scholar 

  19. Momose, F.: On thel-adic representations attached to modular forms. J. Fac. Sci., Univ. Tokyo, Sect. I A,28, 89–109 (1981)

    Google Scholar 

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

    Google Scholar 

  21. Perrin-Riou, B.: Travaux de Kolyvagin et Rubin. Séminaire Bourbaki exposé 717, 1989/90

  22. Ribet, K.: Galois representations attached to eigenforms with nebentypus, In: (Serre, J.-P., Zagier, D.B. eds.) Modular Functions in one Variable V. (Lect. Notes Math., vol. 601, pp. 17–52) Berlin Heidelberg New York: Springer 1977

    Google Scholar 

  23. Schoen, C.: Complex multiplication cycles on elliptic modular threefolds. Duke Math. J.53, No. 3, 771–794 (1985)

    Google Scholar 

  24. Schoen, C.: Complex multiplication cycles and a conjecture of Beilinson and Bloch. (Preprint 1990)

  25. Schoen, C.: On the computation of the cycle class map for nullhomologous cycles over the algebraic closure of a finite field. (Preprint 1989)

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

    Google Scholar 

  27. Serre, J.-P.: Cohomologie Galoisienne. (Lect. Notes Math., vol. 5) Berlin Göttingen Heidelberg New York: Springer 1964

    Google Scholar 

  28. Serre, J.-P.: Local Fields. (Grad. Texts Math., vol. 67) New York Heidelberg Berlin: Springer 1979

    Google Scholar 

  29. Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Princeton: Princeton University Press: 1971

    Google Scholar 

  30. Tate, J.: Relations betweenK 2 and Galois Cohomology. Invent. Math.36, 257–274 (1976) [SGA 41/2] Deligne, P.: Cohomologie étale. (Lect. Notes Math., vol. 569) Berlin Heidelberg New York: Springer 1977

    Google Scholar 

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Authors and Affiliations

  1. MPI für Mathematik, Gottfried-Claren-Str. 26, W-5300, Bonn 3, Federal Republic of Germany

    Jan Nekovář

  2. Math. Institute, Czechoslovak Academy of Science, Zitná 25, 115 67, Praha 1, ČSFR

    Jan Nekovář

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  1. Jan Nekovář
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Oblatum 11-IX-1990 & 29-IV-1991

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Nekovář, J. Kolyvagin's method for Chow groups of Kuga-Sato varieties. Invent Math 107, 99–125 (1992). https://doi.org/10.1007/BF01231883

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