On subgroups of \(\pi_*(L_2T(1)\wedge M(2))\) at the prime two
type: Item
instance of: scholarly article
title: On subgroups of \(\pi_*(L_2T(1)\wedge M(2))\) at the prime two
zbMATH Open document ID: 1175.55011
author: Ippei Ichigi
author: Katsumi Shimomura
author: Xiangjun Wang
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2009-04-21T00:00:00Z
review text: The Adams-Novikov spectral sequence is a tool that can be, in principle, used to determine the homotopy groups \(\pi_{*}(L_{2}T(1))\) where \(T(1)\) is the Ravenel spectrum and \(L_{2}\) denotes the Bousfield localization with respect to the \(\nu_{2}\)-localized Brown-Peterson spectrum \(\nu_{2}^{-1}BP\). This paper determines the \(s\)-th lines of the Adams-Novikov \(E_{\infty}\)-term for \(s = 0,1\) and \(s > 6\) of the Adams-Novikov spectral sequence converging to \(\pi_{*}(L_{2}T(1) \wedge M(2))\) where \(M(2)\) is the mod \(2^{2}\) Moore spectrum. The proofs are very technical and show just how disordered the \(E_{2}\)-term for \(\pi_{*}(L_2T(1))\) is.
Mathematics Subject Classification ID: 55Q52
Mathematics Subject Classification ID: 55Q45
Mathematics Subject Classification ID: 55Q51
zbMATH DE Number: 5545409
zbMATH Keywords: Bousfield localization
zbMATH Keywords: Brown-Peterson spectrum
zbMATH Keywords: Adams-Novikov spectral sequence
zbMATH Keywords: Ravenel spectrum
reviewed by: Jonathan Hodgson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5545409