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Complex cobordism theory for number theorists

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Book cover Elliptic Curves and Modular Forms in Algebraic Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1326))

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References

  1. J. F. Adams, Stable Homotopy and Generalized Homology, Univ. of Chicago Press, 1974.

    Google Scholar 

  2. J. F. Adams, On the groups J(X), IV, Topology 5(1966), 21–71.

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Devinatz, M. J. Hopkins and J. H. Smith, Nilpotence and stable homotopy theory, to appear.

    Google Scholar 

  4. S. Eilenberg and N. E. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, 1952.

    Google Scholar 

  5. M. Hazewinkel, Formal Groups and Applications, Academic Press, 1978.

    Google Scholar 

  6. M. J. Hopkins, Global methods in homotopy theory, to appear in Proceedings of the Durham Symposium on Homotopy Theory 1985, Cambridge University Press, 1987.

    Google Scholar 

  7. M. J. Hopkins, N. Kuhn and D. C. Ravenel, Morava K-theory and generalized characters for finite groups, to appear.

    Google Scholar 

  8. M. J. Hopkins and J. H. Smith, Periodicity and stable homotopy theory, to appear.

    Google Scholar 

  9. K. Johnson, The Conner-Floyd map for formal A-modules, to appear.

    Google Scholar 

  10. P. S. Landweber, Elliptic cohomology and modular forms, these Proceedings.

    Google Scholar 

  11. P. S. Landweber, Homological properties of comodules over MU *(MU) and BP *(BP), Amer. J. Math. 98 (1976), 591–610.

    Article  MathSciNet  MATH  Google Scholar 

  12. P. S. Landweber, D. C. Ravenel and R. E. Stong, Periodic cohomology theories defined by elliptic curves, to appear.

    Google Scholar 

  13. J. Lubin and J. Tate, Formal complex multiplication in local fields, Ann. of Math. 81 (1965), 380–387.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. A. Mitchell, Finite complexes with A(n)-free cohomology, Topology 24(1985), 227–248.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Ochanine, Sur les genres multiplicatifs définis par des intégrales elliptiques, to appear in Topology.

    Google Scholar 

  16. D. G. Quillen, On the formal group laws of oriented and unoriented cobordism theory, Bull. Amer. Math. Soc., 75 (1969), 1293–1298.

    Article  MathSciNet  MATH  Google Scholar 

  17. D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, 1986.

    Google Scholar 

  18. D. C. Ravenel, Localization with respect to certain periodic homology theories, Amer. J. Math. 106(1984), 351–414.

    Article  MathSciNet  MATH  Google Scholar 

  19. D. C. Ravenel, Localization and periodicity in stable homotopy theory, to appear in Proceedings of the Durham Symposium on Homotopy Theory 1985, Cambridge University Press, 1987.

    Google Scholar 

  20. D. C. Ravenel, Formal A-modules and the Adams-Novikov spectral sequence, J. of Pure and Applied Algebra 32(1984), 327–345.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. H. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.

    Google Scholar 

  22. E. H. Spanier, Algebraic Topology, McGraw-Hill, 1966.

    Google Scholar 

  23. R. E. Stong, Notes on Cobordism Theory, Princeton Univ. Press, 1968.

    Google Scholar 

  24. E. Witten, Elliptic genera and quantum field theory, to appear in Math. Comm. Phys.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Washington, 98195, Seattle, WA

    Douglas C. Ravenel

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  1. Douglas C. Ravenel
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Peter S. Landweber

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© 1988 Springer-Verlag

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Ravenel, D.C. (1988). Complex cobordism theory for number theorists. In: Landweber, P.S. (eds) Elliptic Curves and Modular Forms in Algebraic Topology. Lecture Notes in Mathematics, vol 1326. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078042

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  • DOI: https://doi.org/10.1007/BFb0078042

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-19490-3

  • Online ISBN: 978-3-540-39300-9

  • eBook Packages: Springer Book Archive

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