Draft curriculum

Complex bordism relates the stable homotopy category of spectra to MU_*MU-comodules, also known as quasicoherent sheaves over the moduli stack of formal groups. The height filtration of the latter algebraic categories corresponds to the chromatic filtration of stable homotopy theory. We aim to survey key results by Devinatz-Hopkins-Smith and Goerss-Hopkins-Miller in this field.

• Characteristic classes
• Topological K-theory
• Cobordism
• Orthogonal spectra
• Spectral sequences
• Formal groups laws
• Morava E- and K-theory
• The chromatic filtration
• The nilpotence theorem
• The periodicity theorem
• Deformation theory
• Lubin-Tate spectra
• Galois theory