On the \([p^ k]\)-series in Brown-Peterson homology
type: Item
instance of: scholarly article
title: On the \([p^ k]\)-series in Brown-Peterson homology
zbMATH Open document ID: 0702.55008
DOI: 10.1016/0022-4049(90)90033-E
author: George Nakos
published in: Journal of Pure and Applied Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let BP be the Brown-Peterson spectrum at the prime p and let F(x,y) be its (universal p-typical) formal group law. The [n]-series [n]x\(\in BP_*x\) is defined inductively by \([n]x=F(x,[n-1]x)\) and \([1]x=x\). This series gives the defining relation in the BP-cohomology of the classifying space B\({\mathbb{Z}}/n\) and carries a lot of geometric information. In the present note the author establishes strong divisibility results for the coefficients of \([p^ k]x\). This generalizes results of \textit{D. C. Johnson} [J. Pure Appl. Algebra 48, 263-270 (1987; Zbl 0632.55002)] in the case \(k=1\).
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55T25
Mathematics Subject Classification ID: 55R40
zbMATH DE Number: 4151376
zbMATH Keywords: [p]-series
zbMATH Keywords: Brown-Peterson spectrum
zbMATH Keywords: formal group law
zbMATH Keywords: BP-cohomology of the classifying space
zbMATH Keywords: strong divisibility results for the coefficients of \([p^ k]x\)
reviewed by: Erich Ossa
MaRDI profile type: Publication
cites work: A universal formal group and complex cobordism
cites work: On the [p]-series in Brown-Peterson homology
cites work: Q3667609
full work available at URL: 0022-4049(90)90033-e
OpenAlex ID: W1977296219
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description: scientific article; zbMATH DE number 4151376