An algebraic model for rational torus-equivariant spectra

Details An algebraic model for rational torus-equivariant spectra An algebraic model for rational torus-equivariant spectra

2011-01-13

arxiv.org/abs/1101.2511v3

Mathematics

Algebraic Topology

Version 3: (a) The construction of model structures on diagram categories in Appendix B has been generalized to include all th

Scientific paper

We show that the category of rational G-spectra for a torus G is Quillen equivalent to an explicit small and practical algebraic model, thereby providing a universal de Rham model for rational G-equivariant cohomology theories. The result builds on the first author's Adams spectral sequence, the second author's functors making rational spectra algebraic. There are several steps, some perhaps of wider interest (1) isotropy separation (replacing G-spectra by modules over a diagram of ring G-spectra) (2) change of diagram results (3) passage to fixed points on ring and module categories (replacing diagrams of ring G-spectra by diagrams of ring spectra) (4) replacing diagrams of ring spectra by diagrams of differential graded algebras (5) rigidity (replacing diagrams of DGAs by diagrams of graded rings). Systematic use of cellularization of model categories is central.

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