The localized slice spectral sequence, norms of Real bordism, and the Segal conjecture
The localized slice spectral sequence, norms of Real bordism, and the Segal conjecture
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DOI：
10.1016/j.aim.2022.108804
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发表时间：
2020-08
影响因子：
1.7
通讯作者：
Lennart Meier;Xiaolin Shi;Mingcong Zeng
中科院分区：
文献类型：
--
作者：
Lennart Meier;Xiaolin Shi;Mingcong Zeng
在本文中，我们介绍了局部切片谱序列，它是等变切片谱序列的一种变体，用于计算配备残差组动作的几何不动点。我们证明了局域切片谱序列的收敛和恢复定理，并用它来分析实波谱的范数。因此，我们将 Real bordism 谱及其范数与 C 2-Segal 猜想的一种形式联系起来。我们计算了 B P R 的 C 4-范数在一定范围内的局部切片谱序列，并表明 Hill-Hopkins-Ravenel 切片微分与 N 1 2 H F 2 的 Tate 微分族一一对应。
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 B P R in a range and show that the Hill–Hopkins–Ravenel slice differentials are in one-to-one correspondence with a family of Tate differentials for N 1 2 H F 2.