Inventiones mathematicae

, Volume 109, Issue 1, pp 307–327 | Cite as

A finiteness theorem for the symmetric square of an elliptic curve

  • Matthias Flach
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bloch, S., Ogus, A.: Gersten's Conjecture and the homology of schemes. Ann. Sci. Éc. Norm. Supér4, 181–202 (1974)Google Scholar
  2. 2.
    Bloch, S.: A note on Gersten's conjecture in the mixed characteristic case. In: Bloch, S. et al. (eds.) Applications of Algebraic K-theory to Number theory and Algebraic Geometry. Boulder 1983. (Contemp. Math. vol. 55) Providence, RI: Am. Math. Soc. 1985Google Scholar
  3. 3.
    Bloch, S., Kato, K.: L-functions and Tamagawa numbers of motives. In Cartier, P. et al (eds.) The Grothendieck Festschrift, vol. 1. Boston Basel Stuttgart: Birkhäuser 1990Google Scholar
  4. 4.
    Brown, K. S.: Cohomology of Groups. (Grad. Texts Math., vol. 87) Berlin Heidelberg New York: Springer 1982Google Scholar
  5. 5.
    Coates, J., Schmidt, C.G.: Iwasawa theory for the symmetric square of an elliptic curve. J. Reine Angew. Math.375/376, 104–156 (1987)Google Scholar
  6. 6.
    Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. in: Deligne, P., Kuyk, W. (eds.) Modular Functions of One Variable II. (Lect. Notes Math., vol. 349) Berlin Heidelberg New York: Springer 1973Google Scholar
  7. 7.
    Edixhoven, B.: On the Manin constant of modular elliptic curves. In: van der Geer, G., Oort, F., Steenbrink, J. (eds.) Arithmetic Algebraic Geometry. (Prog. Math., vol. 89) Boston Basel Stuttgart: Birkhäuser 1991Google Scholar
  8. 8.
    Faltings, G.: Crystalline Cohomology and p-adic Galois representations. In: Igusa, Jun-Ichi (ed.) Algebraic Analysis, Geometry and Number Theory. Baltimore: The John Hopkins University Press 1991Google Scholar
  9. 9.
    Flach, M.: Selmer groups for the symmetric square of an elliptic curve. Ph.D. dissertation, University of Cambridge (1990)Google Scholar
  10. 10.
    Flach, M.: A generalisation of the Cassels-Tate pairing. J. Reine Angew. Math.412, 113–127 (1990)Google Scholar
  11. 11.
    Gross, B.H.: Kolyvagin's work on modular elliptic curves. In: Coates, J., Taylor, M. (eds.) L-functions and Arithmetic. (Lond. Math. Soc. Lect. Note Ser., vol. 153) Cambridge London: Cambridge University Press 1991Google Scholar
  12. 12.
    Grothendieck, A.: Le groupe de Brauer III. In: Dix exposes sur la cohomologie des schemas pp. 88–188. Amsterdam: North Holland 1968Google Scholar
  13. 13.
    Hida, H.: Congruences of Cusp Forms and Special Values of Their Zeta Functions. Invent. Math.63, 225–261 (1981)Google Scholar
  14. 14.
    Hochschild, G., Serre, J.P.: Cohomology of Group Extensions. Trans. Am. Math. Soc.74, 110–134 (1953)Google Scholar
  15. 15.
    Jannsen, U.: Continuous étale cohomology. Math. Ann.280, 207–245 (1988)Google Scholar
  16. 16.
    Jannsen, U.: Mixed Motives and Algebraic K-theory. (Lect. Notes Math., vol. 1400) Berlin Heidelberg New York: Springer 1990Google Scholar
  17. 17.
    Katz, N., Mazur, B.: Arithmetic moduli of elliptic curves. Princeton: Princeton University Press 1985Google Scholar
  18. 18.
    Mazur, B.: Deformations of Galois representations. In: Ihara, Y. et al. (eds.) Galois Groups over ℝ. (Publ. Math. Sci. Res. Inst. vol. 16) New York: Springer 1989Google Scholar
  19. 19.
    Mildenhall, S.: Cycles in a product of elliptic curves, and a group analogous to the class group. (Preprint 1991)Google Scholar
  20. 20.
    Milne, J.S.: Arithmetic Duality Theorems. (Perspect. Math., vol. 1) Academic Press 1986Google Scholar
  21. 21.
    Quillen, D.: Higher algebraic K-Theory I. In: Bass, H. (ed.) Algebraic K-Theory I. (Lect. Notes Math. vol. 341, pp. 85–147) Berlin Heidelberg New York: Springer 1973Google Scholar
  22. 22.
    Raskind, W.: Torsion algebraic cycles on varieties over local fields. In: Jardine, J.F., Snaith, V.P. (eds.) Algebraic K-Theory: Connections with Geometry and Topology, pp. 343–388. Dordrecht: Kluver Academic Publishers 1989Google Scholar
  23. 23.
    Scholl, A.J.: On Modular Units. Math. Ann.285, 503–510 (1989)Google Scholar
  24. 24.
    Serre, J.P.: Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Invent. Math.15, 259–331 (1972)Google Scholar
  25. 25.
    Sherman, C.: Some theorems on the K-theory of coherent sheaves. Commun. Algebra714, 1489–1508 (1979)Google Scholar
  26. 26.
    Shimura, G.: The special values of zeta functions associated with cusp forms. Commun. Pure Appl. Math.29, 783–804 (1976)Google Scholar
  27. 27.
    Zagier, D.B.: Modular Parametrizations of elliptic curves. Canad. Math. Bull.28 (3), 372–384 (1985)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Matthias Flach
    • 1
  1. 1.Mathematisches InstitutUniversität HeidelbergHeidelbergGermany

Personalised recommendations