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

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 $H_{\ast }(e_n;{\mathbb{F}}_p)$ for any prime $p$ and $n\le 4$ up to possible multiplicative extensions. In order to accomplish this we show that the Künneth 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.

arXiv comment21 pages. Improved exposition and minor corrections