Spanier–Whitehead duality in the 𝐾(2)-local category at 𝑝=2,Proceedings of the American Mathematical Society

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Spanier–Whitehead duality in the 𝐾(2)-local category at 𝑝=2
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-09-04 , DOI: 10.1090/proc/15078
Irina Bobkova

Abstract:The fixed point spectra of Morava

-theory

under the action of finite subgroups of the Morava stabilizer group $\mathbb{G}_n$ , and their

-local Spanier-Whitehead duals can be used to approximate the

-local sphere in certain cases. For any finite subgroup

of $\mathbb{G}_2$ at

we prove that the

-local Spanier-Whitehead dual of the spectrum $E_2^{hF}$ is $\Sigma ^{44}E_2^{hF}$ . These results are analogous to the known results at height 2 and

. The main computational tool we use is the topological duality resolution spectral sequence for the spectrum $E_2^{h\mathbb{S}_2^1}$ at

中文翻译：

ni（2）-局部类别中，-= 2时的Spanier-Whitehead对偶

摘要：摩拉瓦的固定点的光谱

-理论

摩拉瓦稳定剂组的有限子群的作用下，和它们的-local斯巴涅尔-白石偶可以用来近似在某些情况下-local球体。对于at的任何有限子组，我们证明-频谱的-Spanier-Whitehead对偶是。这些结果类似于高度2和处的已知结果。我们使用的主要计算工具是频谱的拓扑偶分解谱序列的。 $\ mathbb {G} _n$

$\ mathbb {G} _2$

$E_2 ^ {hF}$ $\ Sigma ^ {44} E_2 ^ {hF}$

$E_2 ^ {h \ mathbb {S} _2 ^ 1}$

更新日期：2020-11-09

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