Planned lectures

  1. J. Silverman, "The arithmetic of elliptic curves", Springer-Verlag, GTM 106

    2. Algebraic curves, Riemann-Roch theorem, elliptic curves, Weierstrass canonical form, Eisenstein series, discriminant, j-invariant, group structure, the ring of modular forms
  2. D. C. Ravenel, "Nilpotence and periodicity in stable homotopy theory", Princeton University Press, Study 128

    3. The category of formal groups, additive and multiplicative examples, Euler's elliptic formal group law, Lie groups, the formal group of an elliptic curve, p-series, height, classification, Lazard's ring, the universal formal group law
  3. M. J. Hopkins and M. E. Mahowald, "From elliptic curves to homotopy theory", preprint 1998

    4. The supersingular elliptic curve over F4, its formal group, its automorphism group, the universal deformation over WF4[[a]][u, u-1], the Morava stabilizer group
  4. J. F. Adams, "The stable homotopy category", Chicago notes, part III

    5. M. Mahowald, "Thom spectra which are ring spectra"
    Generalized homology theories, spectra, ring spectra, H, KU, KO, Thom spectra, Ainfty ring spectra
  5. J. W. Milnor, "The Steenrod algebra and its dual", Ann. of Math. (1958)

    6. The Steenrod algebra A, its dual, the sub-algebras An
  6. J. Boardman, "Conditionally convergent spectral sequences", preprint

    7. Exact couples, spectral sequences, convergence, the classical Adams spectral sequence, ExtA
  7. J. W. Milnor, "On the cobordism ring Omega* and a complex analogue", Amer. J. Math. (1960)

    8. The complex cobordism ring MU*
  8. J. F. Adams, "Quillen's work on formal groups", Chicago notes, part II

    9. Complex oriented theories, their associated formal group laws, Quillen's theorem
  9. D. C. Ravenel, "Complex cobordism and stable homotopy groups of spheres, Academic Press

    10. Landweber's exact functor theorem, the Brown-Peterson spectrum BP, the E(n), the Morava K-theories, the chromatic filtration
  10. C. Rezk, "Notes on the Hopkins-Miller theorem", preprint

    11. Lubin-Tate theory, universal deformation of formal group laws, the ring spectra En, the Hopkins-Miller Ainfty obstruction theory, the ring spectra EOn, the Goerss-Hopkins Einfty obstruction theory
  11. M. J. Hopkins and M. E. Mahowald, "From elliptic curves to homotopy theory", preprint 1998

    12. The homotopy fixed points (= Adams-Novikov) spectral sequence for (EO2)*, topological modular forms
  12. D. C. Ravenel, "Complex cobordism and stable homotopy groups of spheres", Academic Press

    13. The Adams spectral sequence for generalized homology theories
  13. The E2-term of the Adams-Novikov spectral sequence for EO2
  14. The differentials in the Adams-Novikov spectral sequence for EO2
  15. A. Iwai and N. Shimada, "On the cohomology of some Hopf algebras", Nagoya Math. J. (1967)

    16. D. M. Davis and M. E. Mahowald, "Ext over the subalgebra A2 of the Steenrod algebra for stunted projective spaces"
    The connective spectrum eo2, H*(eo2) = A//A2
  16. The E2-term of the Adams spectral sequence for eo2, Ext over A2
  17. The differentials in the Adams spectral sequence for eo2
  18. The Hurewicz image in (eo2)* and v2-periodic families in pi*S
John Rognes / January 14th 1999