Mathematische Zeitschrift

, Volume 201, Issue 3, pp 401–428 | Cite as

Forms ofK-theory

  • Jack Morava


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adams, J.F.: Lectures on Quillen's Work. Lecture Notes, University of Chicago 1970Google Scholar
  2. 2.
    Atiyah, M.F., Hirzebruch F.: Charakteristische — Klassen und Kohomologie — Operationen. Math. Z.77, 149–187 (1961)Google Scholar
  3. 3.
    Atiyah, M.F., Segal, G.B.: EquivariantK-theory and completion. J. Diff. Geometry3, 1–18 (1969)Google Scholar
  4. 4.
    Atiyah, M.F., Singer, I.M.: The index of elliptic operators I. Ann. Math.87, 484–530 (1968)Google Scholar
  5. 5.
    Atiyah, M.F., Tall, D.O.: Group representations λ-rings, and theJ-homomorphism. Topology8, 253–297 (1969)Google Scholar
  6. 6.
    Birch, B.J., Swinnerton-Dyer, H.P.F.: Notes on Elliptic Curves II. J Reine Angew. Math.218, 79–108 (1965)Google Scholar
  7. 7.
    Cartier, P.: Groupes formels, fonctions automorphes, et fonctions zeta. Nice Proceedings, vol. 2, 291–299. Paris: Gauthier-Villars 1971Google Scholar
  8. 8.
    Fröhlich, A.: Formal groups. Lect. Notes Math. vol. 74. Berlin Heidelberg New York: Springer 1964Google Scholar
  9. 9.
    Hasse, H.: Vorlesungen, über Zahlentheorie ( 2 Auflage). Berlin Heidelberg New York: Springer 1964Google Scholar
  10. 10.
    Hazewinkel, M.: Constructing formal groups I: Report 7119 (with Appendix) of the Economic Institute, Netherlands School of Economics, RotterdamGoogle Scholar
  11. 11.
    Hill, W.L.: Formal groups and zeta-functions of elliptic curves. Invent. Math.12, 321–336 (1971)Google Scholar
  12. 12.
    Hirzebruch, F.: Topological Methods in Algebraic Geometry. Berlin Heidelberg New York: Springer 1966Google Scholar
  13. 13.
    Honda, T.: Formal groups and zeta-functions. Osaka J. Math.5, 199–213 (1968)Google Scholar
  14. 14.
    Honda, T.: On the theory of commutative formal groups. J. Math. Soc. Japan22, 213–245 (1970)Google Scholar
  15. 15.
    Katz, N.: Lectures onp-adic modular forms (to appear in the Notes of the Antwerp Conference, published by Springer)Google Scholar
  16. 16.
    Landweber, P.: Associated prime ideals and Hopf algebras. J. Pure Appl. Algebra3, 43–59 (1973)Google Scholar
  17. 17.
    Landweber, P.: Homological dimension of complex bordism modules. Rutgers University (preprint 1973)Google Scholar
  18. 18.
    Lang, S.: Algebraic Number Theory. Reading, Mass.: Addison-Wesley 1970Google Scholar
  19. 19.
    Lubkin, J., Tate, J.: Formal Moduli for Formal One-Parameter Lie Groups Bull. Soc. Math. Fr.94, 49–60 (1966)Google Scholar
  20. 20.
    Milnor, J., Moore, J.: On the structure of Hopf algebras. Ann. Math.81, 211–264 (1965)Google Scholar
  21. 21.
    Miscenko, A.S.: Nice proceedings, vol. 2, p. 117. Paris: Gauthier-Villars 1971Google Scholar
  22. 22.
    Quillen, D.G.: Elementary proofs of some properties of complex cobordism .... Adv. Math.7, 29–56 (1976).Google Scholar
  23. 23.
    Roquette, P.: Analytic theory of elliptic functions over local fields. Hamburger Mathematische Einzelschriften 1, Göttingen 1971Google Scholar
  24. 24.
    Serre, J.P.: Cours d'arithmetique. Presses Universitaires de FranceGoogle Scholar
  25. 25.
    Wilson, W.S.: The Ω-spectrum for Brown-Peterson cohomology I. Commun. Math. Helvetici.4, 45–55 (1973)Google Scholar

Supplementary References

  1. S1.
    Baker, A.: Hecke operators as operations in elliptic cohomology. Preprint, Manchester University 1988Google Scholar
  2. S2.
    Baker, A.: On the homotopy type of the spectrum representing elliptic cohomology. Preprint, Manchester University 1988Google Scholar
  3. S3.
    Bott, R., Taubes, C.: On the rigidity theorems of Witten. Journal of the AMS2, 137–186 (1989)Google Scholar
  4. S4.
    Brylinski, J.L.: Representations, of loop groups, Dirac operators on loop spaces, and modular forms. Preprint, Brown University 1988Google Scholar
  5. S5.
    Devinatz, E., Hopkins, M., Smith, J.: Nilpotence in stable homotopy I. Ann. Math.128, 207–241 (1988)Google Scholar
  6. S6.
    Hirzebruch, F.: Elliptic genera of levelN for complex manifolds. Preprint, Universität Bonn 1988Google Scholar
  7. S7.
    Hopkins, M., Kuhn, N., Ravenel, D.: Complex oriented cohomology of classifying spaces PreprintGoogle Scholar
  8. S8.
    Katz, N., Mazur, B.: Arithmetic moduli of elliptic curves Ann. Math. Study 108. Princeton: University Press 1985Google Scholar
  9. S9.
    Landweber, P. (ed.): Elliptic curves and modular forms in elliptic cohomology. Lect. Notes Math. 1326 (1988).Google Scholar
  10. S10.
    Mason, G.: Finite Groups and modular functions. Proc. Symposium in Pure Maths. vol. 47 (Part I), 181–210, AMS 1987Google Scholar
  11. S11.
    Miller, H.: The elliptic character and the Witten genus. Preprint, MIT 1988Google Scholar
  12. S12.
    Morava, J.: A product for the odd-primary cobordism of manifolds with singularities. Topology18, 177–186 (1979)Google Scholar
  13. S13.
    Morava, J.: Noetherian localizations of categories of cobordism complexes. Ann. Math.121, 1–39 (1985).Google Scholar
  14. S14.
    Nishida, G.: Modular forms and the double transfer for BT2. Prepritt, Kyoto University 1988Google Scholar
  15. S15.
    Norton, S.: Generalized moonshine, Appendix, to S10 aboveGoogle Scholar
  16. S16.
    Ravenel, D.: Complex cobordism and the stable homotopy of spheres. New York: Academic Press 121, 1986Google Scholar
  17. S17.
    Robinson, A.: Obstruction theory and the strict associativity of MoravaK-theories. Preprint, University of Warwick 1988Google Scholar
  18. S18.
    Segal, G.: Elliptic cohomology. Seminar Bourbaki no. 695, 1988Google Scholar
  19. S19.
    Serre, J.-P.: Oeuvres, Vol. II. Berlin Heidelberg New York: Springer 1986Google Scholar
  20. S20.
    Tamanoi, H.: Hyperelliptic genera, Thesis. The Johns Hopkins University 1987Google Scholar
  21. S21.
    Waldhausen, F.: Algebraic K-theory of spaces, localization and the chromatic filtration of spaces, in Algebraic topology. In: Madsen, I., Oliver, B. (eds.) Algebraic topology. Proceedings, Aarhus 1982 (Lect. Notes Math., vol 1051) Berlin Heidelberg New York: Springer 1984Google Scholar
  22. S22.
    Witten, E.: Elliptic genera and quantum field theory. Commun. Math. Phys. 109, 525–536 (1987)Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Jack Morava
    • 1
  1. 1.Department of MathematicsThe Johns Hopkins UniversityBaltimoreUSA

Personalised recommendations