Title: The homotopy groups of the L2-localized mod 3 Moore spectrum
Abstract:At each prime number p, the homotopy groups π*(L2S0) of the v2−1BP-localized sphere spectrum play an crucial role to understand the category of v2−1BP-local spectra. For p>3, they are determined by us...At each prime number p, the homotopy groups π*(L2S0) of the v2−1BP-localized sphere spectrum play an crucial role to understand the category of v2−1BP-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, π*(L2V(1)) is also determined by using the ANSS, in which E∞=E10 in this case. Here V(1) denotes the Toda-Smith 4-cells spectrum. In this paper, we determine the homotopy groups π*(L2V(0)) of the mod 3 Moore spectrum from π*(L2V(1 )) by the Bockstein spectral sequence (BSS). Actually, we first compute the E2-term of the ANSS by the BSS and then study the Adams-Novikov differentials, and obtain E∞=E10 as well.Read More