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

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2023-01-01 DOI:10.4310/hha.2023.v25.n2.a8

Lukas Katthän, Sean Tilson

引用次数: 0

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 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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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

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.