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The first line of the Bockstein spectral sequence on a monochromatic spectrum at an odd prime

Published online by Cambridge University Press:  11 January 2016

Ryo Kato  and
Katsumi Shimomura
Ryo Kato
Affiliation:
Graduate school of Mathematics, Nagoya University, Aichi, 464-8601, Japan, ryo_kato_1128@yahoo.co.jp
Katsumi Shimomura
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, Kochi, 780-8520, Japan, katsumi@math.kochi-u.ac.jp
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Abstract

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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 of the spectral sequence is an Ext group of BP*BP-comodules. There is a sequence of Ext groups for nonnegative integers n with and there are Bockstein spectral sequences computing a module (n – s) from So far, a small number of the E1-terms are determined. Here, we determine the for p > 2 and n > 3 by computing the Bockstein spectral sequence with E1-term 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).

Keywords

55Q9955T9955Q45
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 207 , September 2012 , pp. 139 - 157
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

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