Rational SU(3)-equivariant cohomology theories

Abstract

We describe the spectral space of conjugacy classes of subgroups of SU(3), together with the additional structure of a sheaf of rings and a component structure. It is a disjoint union of 18 blocks each dominated by a subgroup. For each of these blocks we identify a sheaf of rings and component structure. Taken together, this gives an abelian category A(SU(3)) designed to reflect the structure of rational SU(3)-equivariant cohomology theories, and we assemble the results from elsewhere to show that the category of rational SU(3)-spectra is Quillen equivalent to the category of differential graded objects of A(SU(3)).