Nagoya Mathematical Journal

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

Ryo Kato and Katsumi Shimomura

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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 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).

Article information

Nagoya Math. J., Volume 207 (2012), 139-157.

First available in Project Euclid: 26 July 2012

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Zentralblatt MATH identifier

Primary: 55Q99: None of the above, but in this section
Secondary: 55T99: None of the above, but in this section 55Q45: Stable homotopy of spheres


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

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