The chromatic \(E_1\)-term \(H^0 M_1^2\) for \(p>3\)
type: Item
instance of: scholarly article
title: The chromatic \(E_1\)-term \(H^0 M_1^2\) for \(p>3\)
zbMATH Open document ID: 0940.55018
author: Hirofumi Nakai
published in: The New York Journal of Mathematics
publication date: 2000-03-02T00:00:00Z
full work available at URL: https://eudml.org/doc/120413
full work available at URL: 6-2nf.htm
review text: The chromatic spectral sequence was introduced by Miller, Ravenel and Wilson to compute the \(E_2\)-term \(E^*_2(V(n- 1))\) of the Adams-Novikov spectral sequence converging to the homotopy groups \(\pi_*(V(n))\) at the prime \(p\). Here \(V(n)\) denotes the Smith-Toda spectrum, and is known to exist for \(n\leq 3\) and \(p>2n\). The \(E_1\)-term of the chromatic spectral sequence is written as \(H^t H^s_n\), which is studied when \(s= 0\), \(s+ n\leq 2\) or \((s,t)= (1,0)\). In this paper, the module structure of \(H^0 M^2_1\) is determined at a prime \(>3\). The result and the proof show how complicated the structure is. The proof is analogous to the determination of \(H^0 M^2_0\) by Miller, Ravenel and Wilson, while the computation is much harder. This result is also related to the homotopy groups \(\pi_*(L_3 V(0))\) and \(\pi_*(V(0))\) by the Adams-Novikov spectral sequence, where \(L_3\) denotes the Bousfield localization functor with respect to \(v^{-1}_3 BP\).
reviewed by: Katsumi Shimomura
Mathematics Subject Classification ID: 55Q45
Mathematics Subject Classification ID: 55T15
Mathematics Subject Classification ID: 55N22
Mathematics Subject Classification ID: 55Q51
zbMATH DE Number: 1409629
zbMATH Keywords: stable homotopy of spheres
zbMATH Keywords: Adams-Novikov spectral sequence
zbMATH Keywords: chromatic spectral sequence
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1409629