定域切片谱序列、实边范数和Segal猜想
The localized slice spectral sequence, norms of Real bordism, and the Segal conjecture
摘要：
在本文中，我们介绍了本地化的切片谱序列，一个变种的等变切片谱序列，计算几何不动点配备剩余群作用。证明了局部切片谱序列的收敛性和恢复性定理，并用它分析了实边谱的范数。因此，我们涉及到的实bordism频谱和其规范的形式的$C_2$ -西格尔猜想。我们计算了$BP_\mathbb{R}$的$C_4$ -范数在一定范围内的局部切片谱序列，并证明了Hill-Hopkins-Ravenel切片微分与$N_1^2 H{\mathbb{F}}_2$的Tate微分族是一一对应的.
英文摘要：
In this paper, we introduce the localized slice spectral sequence, a variant of the equivariant slice spectral sequence that computes geometric fixed points equipped with residue group actions. We prove convergence and recovery theorems for the localized slice spectral sequence and use it to analyze the norms of the Real bordism spectrum. As a consequence, we relate the Real bordism spectrum and its norms to a form of the $C_2$-Segal conjecture. We compute the localized slice spectral sequence of the $C_4$-norm of $BP_\mathbb{R}$ in a range and show that the Hill--Hopkins--Ravenel slice differentials is in one-to-one correspondence with a family of Tate differentials for $N_1^2 H{\mathbb{F}}_2$.
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