Planned lectures

J. Silverman, "The arithmetic of elliptic curves", SpringerVerlag, GTM
106
Algebraic curves, RiemannRoch theorem, elliptic curves, Weierstrass
canonical form, Eisenstein series, discriminant, jinvariant, group structure,
the ring of modular forms

D. C. Ravenel, "Nilpotence and periodicity in stable homotopy theory",
Princeton University Press, Study 128
The category of formal groups, additive and multiplicative examples,
Euler's elliptic formal group law, Lie groups, the formal group of an elliptic
curve, pseries, height, classification, Lazard's ring, the universal formal
group law

M. J. Hopkins and M. E. Mahowald, "From elliptic curves to homotopy theory",
preprint 1998
The supersingular elliptic curve over F_{4}, its formal group,
its automorphism group, the universal deformation over WF_{4}[[a]][u,
u^{1}], the Morava stabilizer group

J. F. Adams, "The stable homotopy category", Chicago notes, part III
M. Mahowald, "Thom spectra which are ring spectra"
Generalized homology theories, spectra, ring spectra, H, KU, KO, Thom
spectra, A_{infty }ring spectra

J. W. Milnor, "The Steenrod algebra and its dual", Ann. of Math. (1958)
The Steenrod algebra A, its dual, the subalgebras A_{n}

J. Boardman, "Conditionally convergent spectral sequences", preprint
Exact couples, spectral sequences, convergence, the classical Adams
spectral sequence, Ext_{A}

J. W. Milnor, "On the cobordism ring Omega^{*} and a complex analogue",
Amer. J. Math. (1960)
The complex cobordism ring MU_{*}

J. F. Adams, "Quillen's work on formal groups", Chicago notes, part II
Complex oriented theories, their associated formal group laws, Quillen's
theorem

D. C. Ravenel, "Complex cobordism and stable homotopy groups of spheres,
Academic Press
Landweber's exact functor theorem, the BrownPeterson spectrum BP,
the E(n), the Morava Ktheories, the chromatic filtration

C. Rezk, "Notes on the HopkinsMiller theorem", preprint
LubinTate theory, universal deformation of formal group laws, the
ring spectra E_{n}, the HopkinsMiller A_{infty} obstruction
theory, the ring spectra EO_{n}, the GoerssHopkins E_{infty}
obstruction theory

M. J. Hopkins and M. E. Mahowald, "From elliptic curves to homotopy theory",
preprint 1998
The homotopy fixed points (= AdamsNovikov) spectral sequence for (EO_{2})_{*},
topological modular forms

D. C. Ravenel, "Complex cobordism and stable homotopy groups of spheres",
Academic Press
The Adams spectral sequence for generalized homology theories

The E_{2}term of the AdamsNovikov spectral sequence for EO_{2}

The differentials in the AdamsNovikov spectral sequence for EO_{2}

A. Iwai and N. Shimada, "On the cohomology of some Hopf algebras", Nagoya
Math. J. (1967)
D. M. Davis and M. E. Mahowald, "Ext over the subalgebra A_{2}
of the Steenrod algebra for stunted projective spaces"
The connective spectrum eo_{2}, H^{*}(eo_{2})
= A//A_{2}

The E_{2}term of the Adams spectral sequence for eo_{2},
Ext over A_{2}

The differentials in the Adams spectral sequence for eo_{2}

The Hurewicz image in (eo_{2})_{*} and v_{2}periodic
families in pi_{*}^{S}
John Rognes / January 14th 1999