Acyclicity of BP-related homologies and cohomologies
type: Item
instance of: scholarly article
title: Acyclicity of BP-related homologies and cohomologies
zbMATH Open document ID: 0577.55004
author: Zen-ichi Yosimura
published in: Osaka Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: \textit{D. Ravenel} [Am. J. Math. 106, 351-414 (1984)] initiated a study of Bousfield classes of Brown-\(Peterson\)-\(related\) spectra. The Bousfield class of the spectrum E, \(<E>\), consists of those spectra F satisfying the following relation for all spectra \(X: F_*X=0\) if and only if \(E_*X=0\). One can also define a cohomology Bousfield class of E, \(<E>^*\), whose members F satisfy the analogous relation: \(F^*X=0\) if and only if \(E^*X=0\). For any p-local spectrum E, there is an Anderson dual spectrum \(\nabla E\) for which \(<\nabla E>^*=<E>\). When does \(<\nabla E>=<E>^* ?\) The author shows that \(<\nabla E>=<E>^*\) if E is one of the friendly Brown-\(Peterson\)-\(related\) spectra \(BP<n>\), E(n), P(n), B(n), and k(n). This equality does not hold for certain infinite products of these spectra.
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 55P42
zbMATH DE Number: 3923671
zbMATH Keywords: localization with respect to homology
zbMATH Keywords: Bousfield classes of Brown- \(Peterson\)-\(related\) spectra
zbMATH Keywords: cohomology Bousfield class
reviewed by: David C. Johnson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3923671