Audio files and slides from Jack Morava's birthday conference
The Newton Institute proceedings
This page compiles a list of suggested reading for the upcoming Talbot workshop on the construction of tmf. Many of the documents here are preliminary versions of papers, which I have posted with the kind permission of the authors. For subjects where I did not know any printed references, there are scanned notes from seminars and workshops, whose contents should be viewed with even more caution.
Segal: Bourbaki and the long version of the Bourbaki article
Jens Franke: On the construction of elliptic cohomology, Math. Nachr. 158, 1992, pp.43-65.
P.S. Landweber, D.C. Ravenel, R.E. Stong, Periodic cohomology theories defined by elliptic curves, Contemporary Mathematics 181, 1995, pp.317-337.
P.S. Landweber (Editor), Elliptic curves and Modular Forms in Algebraic Topology: Proceedings, Priceton 1986, LNM 1326, Springer-Verlag, Berlin, 1986.
Matthew Greenberg's Master's thesis: Constructing elliptic cohomology
Jacob Lurie: A Survey of Elliptic Cohomology
Mike Hopkins (ICM 2002): Algebraic Topology and Modular Forms
Haynes Miller (slides from a talk in Barcelona, 2002) Elliptic Cohomology: A Perspective and Some Prospects
Mike Hopkins (Notes from a talk at Santa Barbara): Algebraic Topology and Differential FormsStefan Schwede's notes from the Muenster Conference: Mike Hopkins I, Mike Hopkins II, Matthew Ando, Charles Rezk, (some Charles Rezk and) Haynes Miller, Haynes Miller II, Paul Goerss I, Paul Goerss II.
Lars Hesselholt's notes from Mike Hopkins' 2004 class on tmf: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10, Part 11, Part 12, Part 13, Part 14, Part 15.
John Rognes: Topologiske Modulaere Former
Hopkins, Miller: Elliptic curves and stable homotopy theory
Hopkins, Miller: On the Hopkins Miller theorem
Mike Hopkins (lecture notes): Course Notes for Elliptic Cohomology
Paul Goerss, Charles Rezk: Bonn lectures
Charles Rezk: Supplementary Notes for Math 152
M. Hopkins and M. Mahowald: From Elliptic Curves to Homotopy Theory, preprint, MIT and Northwestern University, June 1998
The book by Thomas: Ellliptic cohomology
E.S. Devinatz and M.H. Hopkins Homotopy fixed point spectra for closed subgroups of the Morava Stabilizer groups
Charles Rezk Notes on the Hopkins-Miller Theorem
Mark Mahowald and Charles Rezk: topological modular forms at level 3.Paul Goerss: (Pre-)sheaves of ring spectra over the moduli stack of formal group laws
Mike Hopkins: Complex Oriented Cohomology Theories and the Language of Stacks
Bertrand Toen, Gabriele Vezzosi: "Brave New" algebraic geometry and global derived moduli spaces of ring spectra
Niko Naumann: Comodule categories and the geometry of the stack of formal groups
Niko Naumann: Quasi-isogenies and Morava stabilizer groups
Haynes Miller: Sheaves and the exact functor theorem
A seminar talk by Jacob Lurie on the role of stacks in homotopy theory and the Landweber exact functor theorem: Part 1 Part 2
Paul Goerss and Mike Hopkins: Moduli spaces of commutative ring spectra
Paul Goerss and Mike Hopkins: Moduli Problems for structured ring spectra
Gerd Laures: K(1)-local Topological Modular Forms
Mike Hopkins: K(1)-local E_oo Ring Spectra
Some of this can be found in Hovey Strickland: Morava K-theories and localizations. This paper also is the only one with a phantom discussion which is strong enough to deal with the construction of the Morava E-theories.
Another reference that speaks about the K(2)-local picture are the Bonn notes by Goerss-Rezk (above) and the string orientation paper by Ando-Hopkins-Rezk below.Here are a few handwritten notes from a seminar talk on the topic:
Talk on the construction of tmf, the K(2)-localization of tmf ...
... notes from a conversation with Mike ... and ... a second conversation with Mike ... (both on K(2)-local topological modular forms)
... and a third one ... on K(2) local topological modular forms and the construction of tmf.
Notes from conversations with Johan ... and ... Haynes.
Tilman Bauer: Computation of the homotopy of the spectrum tmf
Tilman Bauer: Elliptic cohomology and projective spaces - a computation -
Ando, Hopkins, Rezk: orientations
Ando, Hopkins, Rezk: MString --> tmf
Ando, Hopkins and Strickland: Elliptic Spectra, the Witten Genus and the Theorem of the Cube
Ginzburg, Kapranov, Vasserot: Elliptic Algebras and Equivariant Elliptic Cohomology
Ioanid Rosu: Equivariant elliptic cohomology and rigidity
David Gepner's thesis: Homotopy topoi and equivariant elliptic cohomology
Greenlees Hopkins Rosu: Rational circle equivariant elliptic cohomology
Jorge Devoto: Equivariant elliptic cohomology and finite groups
Matthew Ando: Equivariant Elliptic Cohomology and Rigidity
Ando, Basterra: The Witten Genus and Equivariant Elliptic Cohomology
Ando: The sigma orientation for analytic circle-equivariant elliptic cohomology
Charles Rezk (MIT notes): Notes on power operations
Matthew Ando: Power Operations in Elliptic Cohomology and Representations of Loop Groups
Ando, Hopkins, Strickland: The Sigma Orientation is an H_oo-map
Mark Behrens: A modular description of the K(2)-local sphere at the prime 3
Goerss, Henn, Mahowald, Rezk: A resolution of the K(2)-local sphere at the prime 3
Teichner, Stolz: What is an elliptic object?
Po Hu, Igor Kriz: Conformal Field Theory and Elliptic Cohomology
Baas, Dundas, Rognes: Two-Vector bundles and forms of elliptic cohomology