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

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-23 DOI:10.1112/blms.70074

Ian J. Leary, Jason Semeraro

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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 $H^{*} (S; F_{p})$ generated by Chern classes of $F$ -stable representations of $S$ . We show that $Ch (F)$ is contained in $H^{*} (F; F_{p})$ 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 $F$ -stable $S$ -sets.

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融合系统特征类产生的上同调子谱

如果F $\mathcal {F}$是有限p$ p$ -群S$ S$上的饱和融合系统，我们定义F $\mathcal {F}$的chen子带Ch (F)$ {\operatorname{Ch}}(\mathcal {F})$是H∗的子带(5)；F p)$ H^*(S;{\mathbb {F}}_p)$由F $\mathcal {F}$的陈氏类生成- S$ S$的稳定表示。证明了Ch (F)$ {\operatorname{Ch}}(\mathcal {F})$包含在H∗(F；F p)$ H^*(\mathcal {F};{\mathbb {F}}_p)$，并应用Green和第一作者的结果在某一类初等阿贝尔子群上描述其最大理想谱。对于F $\mathcal {F}$ -stable S$ S$ -sets的特征类，我们得到了类似的结果。

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