The First Line of the Bockstein Spectral Sequence on a Monochromatic Spectrum at an Odd Prime
نویسندگان
چکیده
The chromatic spectral sequence is introduced in [8] to compute the E2-term of the Adams-Novikov spectral sequence for computing the stable homotopy groups of spheres. The E1-term E s,t 1 (k) of the spectral sequence is an Ext group of BP∗BP -comodules. There are a sequence of Ext groups E 1 (n − s) for non-negative integers n with E s,t 1 (0) = E s,t 1 , and Bockstein spectral sequences computing a module Es,∗ 1 (n − s) from E s−1,∗ 1 (n − s + 1). So far, a small number of the E1-terms are determined. Here, we determine the E 1 (n−1) = Ext M1 n−1 for p > 2 and n > 3 by computing the Bockstein spectral sequence with E1-term E 0,s 1 (n) for s = 1, 2. As an application, we study the non-triviality of the action of α1 and β1 in the homotopy groups of the second Smith-Toda spectrum V (2).
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