论文标题
在切片频谱序列上，用于真实界限规范的商
On the slice spectral sequence for quotients of norms of Real bordism
论文作者
论文摘要
在本文中，我们通过排列summands调查了真实bordism频谱的乘法规范$ mu^{（（（c_ {2^n}））} $的倍增性型号的均值。这些商很感兴趣，因为它们与更高的$ k $理论有着密切的关系。我们介绍了用于计算此类商的均质均值组的新技术。 作为一个新示例，我们研究了理论$ bp^{（（（c_ {2^n}））} \ langle m，m \ rangle $。这些光谱是结缔组织Morava $ K $理论的自然概括。我们提供了$ i^*_ {c_ {c_ {2^{2^{n-1}}} bp^{（（（（c_ {2^n}）} \ langle m，m，m \ rangle $，其中$ c _ n是$ c__的，我们是$ c__ n是$ c__的，我们提供了$ i^*_ {c_ {2^{2^{n-1}}} bp^{（（（（c_ {2^n}）} \ langle m，m，m，m \ rangle $，其中$ c__ n是$ c__的$ c__的2，为了实现此计算，我们在此局部切片序列与$ h \ Mathbb {f} _2 _2 _2 _2 _2 _2 _2的ADAMS光谱序列之间建立了对应关系。此外，我们提供了$a_λ$局部化的切片频谱序列的完整计算。 $ C_4 $ -SLICE光谱序列可以完全从该计算中恢复。
In this paper, we investigate equivariant quotients of the Real bordism spectrum's multiplicative norm $MU^{((C_{2^n}))}$ by permutation summands. These quotients are of interest because of their close relationship with higher real $K$-theories. We introduce new techniques for computing the equivariant homotopy groups of such quotients. As a new example, we examine the theories $BP^{((C_{2^n}))}\langle m,m\rangle$. These spectra serve as natural equivariant generalizations of connective integral Morava $K$-theories. We provide a complete computation of the $a_σ$-localized slice spectral sequence of $i^*_{C_{2^{n-1}}}BP^{((C_{2^n}))}\langle m,m\rangle$, where $σ$ is the real sign representation of $C_{2^{n-1}}$. To achieve this computation, we establish a correspondence between this localized slice spectral sequence and the $H\mathbb{F}_2$-based Adams spectral sequence in the category of $H\mathbb{F}_2 \wedge H\mathbb{F}_2$-modules. Furthermore, we provide a full computation of the $a_λ$-localized slice spectral sequence of the height-4 theory $BP^{((C_{4}))}\langle 2,2\rangle$. The $C_4$-slice spectral sequence can be entirely recovered from this computation.
