The Adams-Novikov \(E_2\)-term for computing \(\pi_*(L_2 V(0))\) at the prime 2
type: Item
instance of: scholarly article
title: The Adams-Novikov \(E_2\)-term for computing \(\pi_*(L_2 V(0))\) at the prime 2
zbMATH Open document ID: 0931.55009
DOI: 10.1016/S0166-8641(98)00048-0
author: Katsumi Shimomura
published in: Topology and its Applications
publication date: 2000-02-21T00:00:00Z
review text: Let \(V(0)\) denote the mod \(p\) Moore spectrum, let \(E(2)\) stand for the corresponding Johnson-Wilson spectrum with coefficients \(E(2)_* \cong Z_{(p)}[v_1,v_2^{\pm 1}]\), and let \(L_2\) denote the Bousfield localization functor with respect to \(E(2)\). The \(E_2\)-term \(E_2^*(L_{2}V(0))\) of the Adams-Novikov spectral sequence converging to the homotopy groups of \(L_{2}V(0)\) is given by \(E_2^*(L_{2}V(0)) = \text{Ext}^*_{\Gamma}(A,A)\) over the Hopf algebroid \((A,\Gamma) = (E(2)_*, E(2)_*E(2))\). In the present paper the author determines the module structure of \(E_2^*(L_{2}V(0))\) for \(p=2\) using the chromatic spectral sequence.
reviewed by: Michael Joachim
Mathematics Subject Classification ID: 55Q10
Mathematics Subject Classification ID: 55T15
Mathematics Subject Classification ID: 55Q45
Mathematics Subject Classification ID: 55P60
zbMATH DE Number: 1340401
zbMATH Keywords: Adams-Novikov spectral sequence
zbMATH Keywords: mod 2 Moore spectrum
zbMATH Keywords: Bousfield localization
MaRDI profile type: Publication
full work available at URL: s0166-8641(98)00048-0
OpenAlex ID: W2051928916
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description: scientific article; zbMATH DE number 1340401