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

抄録

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.