Suggested reading

Throughout

• Mike Hopkins and Mark Mahowald, From Elliptic Curves to Homotopy Theory,
  preprint, MIT and Northwestern University, June 1998 (here is the PostScript file).

Weeks 4 and 5

For basic material on elliptic curves, read:

• Joseph H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics no. 106, Springer-Verlag, 1986 (available at the Akademika bookstore).
  • Chapter II: Algebraic Curves, II.1 Curves, II.5 The Riemann-Roch Theorem.
  • Chapter III: The Geometry of Elliptic Curves, III.1 Weierstrass Equations, III.2 The Group Law, III.3 Elliptic Curves, III.10 The Automorphism Group.
  • Chapter IV: The Formal Group of an Elliptic Curve, IV.1 Expansion around O, IV.2 Formal Groups, IV.3 Groups Associated to Formal Groups, IV.4 The Invariant Differential, IV.7 Formal Groups in Characteristic p.
  • Appendix C. Section 12 Modular Functions.

Weeks 6 and 7

For material on formal group laws, read one of:

• John Frank Adams, Stable Homotopy and Generalised Homology, Chicago Lectures in Mathematics, The University of Chicago Press, 1974 (available at amazon.com.)
  • Part II: Quillen's work on formal groups and complex cobordism.
• Douglas C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres Pure and Applied Mathematics, Academic Press, Inc., 1986 (out of print, but you may try amazon.com.)
  • Appendix 2: Formal Group Laws.

For the Lubin-Tate deformation theory, I will use the presentation in Charles Rezk's Notes on the Hopkins-Miller theorem.

Week 8

Week 8 (February 22nd - 26th) I'll be in Bielefeld for a workshop.

Weeks 9 and 10

For the Steenrod algebra, exact couples, the Adams spectral sequence, and the complex bordism ring the following may be useful:

• Norman E. Steenrod and D.B.A. Epstein, Cohomology operations,
  Annals of Mathematics Studies no. 50, Princeton University Press, 1962.
• Robert E. Mosher and Martin C. Tangora, Cohomology operations and applications in homotopy theory,
  Harper's Series in Modern Mathematics, Harper and Row, 1968.
• J. Michael Boardman, Conditionally Convergent Spectral Sequences,
  preprint, The Johns Hopkins University, 1981 (paper copy available from John Rognes).
• John W. Milnor, The Steenrod algebra and its dual,
  Ann. of Math., vol. 67, pages 150-171 (1958).
• John W. Milnor, On the cobordism ring $\Omega^*$ and a complex analogue. I,
  Amer. J. Math., vol. 82, pages 505-521 (1960).