论文标题
局部切片频谱序列，真实狂热的规范和Segal猜想
The localized slice spectral sequence, norms of Real bordism, and the Segal conjecture
论文作者
论文摘要
在本文中，我们介绍了局部切片频谱序列，这是Equivariant Slice光谱序列的变体，该序列计算配备了残基组动作的几何固定点。我们证明了局部切片光谱序列的收敛和恢复定理，并使用它来分析真实的bordism光谱的规范。结果，我们将真实的Bordism频谱及其规范与$ C_2 $ -Segal猜想的形式联系起来。我们在范围内计算$ c_4 $ -norm $ bp_ \ mathbb {r} $的本地切片频谱序列，并表明山丘 - 霍普金斯 - 摩尔金烯slice slice差速器在与$ N_1^2 H {\ Mathbb {\ Mathbb {\ m ress的泰特差异家族的一对一中。
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 $N_1^2 H{\mathbb{F}}_2$.
