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September 2012 The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime
Ryo Kato, Katsumi Shimomura
Nagoya Math. J. 207: 139-157 (September 2012). DOI: 10.1215/00277630-1630050

Abstract

The chromatic spectral sequence was introduced by Miller, Ravenel, and Wilson to compute the E2-term of the Adams-Novikov spectral sequence for computing the stable homotopy groups of spheres. The E1-term E1s,t(k) of the spectral sequence is an Ext group of BPBP-comodules. There is a sequence of Ext groups E1s,t(ns) for nonnegative integers n with E1s,t(0)=E1s,t, and there are Bockstein spectral sequences computing a module E1s,(ns) from E1s1,(ns+1). So far, a small number of the E1-terms are determined. Here, we determine the E11,1(n1)=Ext1Mn11 for p>2 and n>3 by computing the Bockstein spectral sequence with E1-term E10,s(n) for s=1,2. As an application, we study the nontriviality of the action of α1 and β1 in the homotopy groups of the second Smith-Toda spectrum V(2).

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Ryo Kato. Katsumi Shimomura. "The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime." Nagoya Math. J. 207 139 - 157, September 2012. https://doi.org/10.1215/00277630-1630050

Information

Published: September 2012
First available in Project Euclid: 26 July 2012

zbMATH: 1277.55007
MathSciNet: MR2957145
Digital Object Identifier: 10.1215/00277630-1630050

Subjects:
Primary: 55Q99
Secondary: 55Q45 , 55T99

Rights: Copyright © 2012 Editorial Board, Nagoya Mathematical Journal

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Vol.207 • September 2012
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