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

2024/04/16 by Ian J. Leary, Leary, Ian J., Jason Semeraro +1
Mathematics · #20D20 #20J06 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2404.10701

openalex publication_date 2024/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If F is a saturated fusion system on a finite p-group S, we define the Chern subring Ch(F) of F to be the subring of the mod-p cohomology H^*(S) of S generated by the Chern classes of F-stable representations of S. We show that Ch(F) is contained in H^*(F) and apply a result of Green and the first author to describe its spectrum in terms of a certain category of elementary abelian subgroups of S. We obtain similar results for various related subrings, including those generated by characteristic classes of F-stable S-sets.

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