的同源性连接摩拉瓦河与系数E理论美元美元\ mathbb {F} _p美元

Pub Date : 2023-01-01 DOI:10.4310/hha.2023.v25.n2.a8
Lukas Katthän, Sean Tilson
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引用次数: 0

摘要

让$e_n$作为Morava的连接覆盖$E$ -理论光谱$E_n$的高度$n$。在本文中,我们计算了它的同调$H_*(e_n;\mathbb{F}_p)$对于任何素数$p$和$n \leq 4$,直到可能的乘法扩展。为了实现这一点,我们表明,当所讨论的$R$ -模块是交换的$S$ -代数时,基于$E_3$ -代数$R$的Kunneth谱序列是乘法的。然后我们通过处理$BP$应用这个结果,这是一个已知的$E_4$ -代数。
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The homology of connective Morava $E$-theory with coefficients in $\mathbb{F}_p$
Let $e_n$ be the connective cover of the Morava $E$-theory spectrum $E_n$ of height $n$. In this paper we compute its homology $H_*(e_n;\mathbb{F}_p)$ for any prime $p$ and $n \leq 4$ up to possible multiplicative extensions. In order to accomplish this we show that the Kunneth spectral sequence based on an $E_3$-algebra $R$ is multiplicative when the $R$-modules in question are commutative $S$-algebras. We then apply this result by working over $BP$ which is known to be an $E_4$-algebra.
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