Topological Automorphic Forms I: definition.

I will review the definition of certain moduli spaces of abelian varieties (Shimura varieties) which generalize the role that the moduli space of elliptic curves plays in number theory. Associated to these Shimura varieties are cohomology theories of Topological Automorphic Forms (TAF) which generalize the manner in which Topological Modular Forms are associated to the moduli space of elliptic curves. These cohomology theories arise as a result of a theorem of Jacob Lurie.

References

• Mark Behrens, Notes on the construction of TMF (2007).
• Mark Behrens and Tyler Lawson, Topological Automorphic Forms, Memoirs of the AMS 958 (2010).
• Paul Goerss, Topological modular forms (after Hopkins, Miller and Lurie), Séminaire Bourbaki, 2009.
• Mike Hopkins, Topological modular forms, the Witten genus and the Theorem of the cube, Proceedings of the 1994 ICM.
• Mike Hopkins, Algebraic Topology and Modular Forms, Proceedings of the 2002 ICM.
• Tyler Lawson, An overview of abelian varieties in homotopy theory (2008).

Doug Ravenel's web page for a seminar on topological automorphic forms contains a comprehensive list of references.