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Equivariant Steinberg summands
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n2.a13
Krishanu Sankar 1
Affiliation  

We construct Steinberg summands of $G$-equivariant spectra with $\mathrm{GL}_n(\mathbb{F}_p)$-action. We prove a lemma about their fixed points when $G$ is a $p$-group, and then use this lemma to compute the fixed points of the Steinberg summand of the equivariant classifying space of $(\mathbb{Z}/p)^n$. These results will be used in a companion paper to study the layers in the mod $p$ symmetric power filtration for $H\underline{\mathbb{F}}_p$.

中文翻译:

等变 Steinberg 求和

我们用 $\mathrm{GL}_n(\mathbb{F}_p)$-action 构造 $G$-等变谱的 Steinberg 求和。当$G$是$p$-群时,我们证明了它们不动点的引理,然后用这个引理计算$(\mathbb{Z}/p)的等变分类空间的Steinberg和的不动点^n$。这些结果将在配套论文中用于研究 $H\underline{\mathbb{F}}_p$ 的 mod $p$ 对称功率过滤中的层。
更新日期:2020-01-01
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