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Algebraic groups and equivariant cohomology theories

Wednesday 11th December 2002 - 09:00 to 10:00
INI Seminar Room 1
Session Title: 
Elliptic cohomology and chromatic phenomena
Equivariant cohomology theories E_G^*(.) are represented by G-spectra. When G is a torus and the theories are rational, there is a complete and calculable algebraic model A(G) of rational G-spectra (based on the idea that E_G^*(.) is built from its behaviour at each isotropy group). This model is formally very similar to a category of sheaves on an algebraic group C. Based on this, one can investigate the properties of cohomology theories E_G^*(.) based on the group C. In several cases of interest (including the case when C is an elliptic curve over a field of characteristic zero and G is the circle group) these properties are sufficient to determine a _construction_ of the cohomology theory using the model A(G).
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons