The Smith-Toda complex \(V((p + 1)/2)\) does not exist
type: Item
instance of: scholarly article
title: The Smith-Toda complex \(V((p + 1)/2)\) does not exist
zbMATH Open document ID: 1194.55017
author: Lee S. Nave
published in: Annals of Mathematics. Second Series
publication date: 2010-05-27T00:00:00Z
full work available at URL: p10.xhtml
review text: Let \(p\) be a prime number. A Smith-Toda complex \(V(k)\) is a finite spectrum with Brown-Peterson homology \(\text{BP}_*/(p,v_1,\ldots,v_k)\), where \(v_1,v_2,\ldots\,\) are the standard generators for \(\text{BP}_*\). For \(p\geq 7\) the author shows that there is no Smith-Toda complex \(V\bigl((p+1)/2\bigr)\); also, if there is a complex \(V\bigl((p-1)/2\bigr)\) then it is not a ring spectrum. The proof uses a generalised homotopy fixed point spectral sequence due to Hopkins and Miller.
reviewed by: Richard John Steiner
Mathematics Subject Classification ID: 55Q51
zbMATH DE Number: 5712733
zbMATH Keywords: Smith-Toda complex
zbMATH Keywords: Haynes-Miller spectral sequence
MaRDI profile type: Publication
OpenAlex ID: W2005367102
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DOI: 10.4007/ANNALS.2010.171.491
description: scientific article; zbMATH DE number 5712733