The Homology of Connective Morava $E$-theory with coefficients in $\mathbb{F}_p$

Lukas Katthän; Sean Tilson

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arXiv · 1704.07248

The Homology of Connective Morava $E$-theory with coefficients in $\mathbb{F}_p$

Lukas Katthän·Sean Tilson

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Abstract

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 K\"unneth 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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BibTeX RIS

Lukas Katthän, Sean Tilson. 2017-04-24. The Homology of Connective Morava $E$-theory with coefficients in $\mathbb{F}_p$. https://arxiv.org/abs/1704.07248

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