发表机构
Indiana University（印第安纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文定义了常值谱Mackey函子，将其等同于某环谱上的模，并显式构造了循环p-群情形，进而计算了等变Steenrod代数。
AI 中文摘要
对于有限群$G$，我们将常值谱$G$-Mackey函子定义为一种真正的$G$-谱，其中范畴不动点之间的限制是等价。我们进一步将常值谱$G$-Mackey函子的全子范畴等同于某个$\nathbb{E}_1$-环谱$R_G$上的模范畴。当$G=C_{p^n}$为循环$p$-群时，我们给出了$\nathbb{E}_1$-环谱$R_{C_{p^n}}$的显式构造。证明使用了真正的$C_{p^n}$-谱的重构定理，该定理可能具有独立的意义。作为应用，我们计算了$\nathbb{Z}$-分次的$C_{p^n}$-等变模$p$ Steenrod代数。
英文摘要
For a finite group $G$, we define a constant spectral $G$-Mackey functor as a genuine $G$-spectrum in which the restrictions between categorical fixed points are equivalences. We further identify the full subcategory of constant spectral $G$-Mackey functors with the category of modules over a certain $\mathbb{E}_1$-ring spectrum $R_G$. When $G=C_{p^n}$ is a cyclic $p$-group, we provide an explicit construction of the $\mathbb{E}_1$-ring spectrum $R_{C_{p^n}}$. The proof uses a reconstruction theorem for genuine $C_{p^n}$-spectra, which might be of independent interest. As an application, we compute the $\mathbb{Z}$-graded $C_{p^n}$-equivariant mod $p$ Steenrod algebra.
Comments42 pages, comments welcome!
