The homotopy groups of the L2-localized mod 3 Moore spectrum

Abstract

At each prime number p, the homotopy groups p�…L2S 0 † of the v y1 2 BP- localized sphere spectrum play an crucial role to understand the category of v y1 2 BP- local spectra. For p > 3, they are determined by using the Adams-Novikov spectral sequence (ANSS), which collapses in this case. At the prime 3, p�…L2V…1†† is also determined by using the ANSS, in which Eyˆ E10 in this case. Here V…1† denotes the Toda-Smith 4-cells spectrum. In this paper, we determine the homotopy groups p�…L2V…0†† of the mod 3 Moore spectrum from p�…L2V…1†† by the Bockstein spectral sequence (BSS). Actually, we ®rst compute the E2-term of the ANSS by the BSS and then study the Adams-Novikov dierentials, and obtain EyE10 as well.