Spectra of subrings of cohomology generated by characteristic classes for fusion systems

Abstract If is a saturated fusion system on a finite ‐group , we define the Chern subring of to be the subring of generated by Chern classes of ‐stable representations of . We show that is contained in and apply a result of Green and the first author to describe its maximal ideal spectrum in terms of a certain category of elementary abelian subgroups. We obtain similar results for various related subrings, including those generated by characteristic classes of ‐stable ‐sets.