The homotopy groups of the L_2localized mod 3 Moore spectrum
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Abstract
At each prime number p, the homotopy groups π<SUB>*</SUB>(L<SUB>2</SUB>S<SUP>0</SUP>) of the v<SUB>2</SUB><SUP>1</SUP>BP localized sphere spectrum play an crucial role to understand the category of v<SUB>2</SUB><SUP>1</SUP>BPlocal spectra. For p>3, they are determined by using the AdamsNovikov spectral sequence (ANSS), which collapses in this case. At the prime 3, \ π<SUB>*</SUB>(L<SUB>2</SUB>V(1)) is also determined by using the ANSS, in which E<SUB>∞</SUB>= E<SUB>10</SUB> in this case. Here V(1) denotes the TodaSmith 4cells spectrum. In this paper, we determine the homotopy groups π<SUB>*</SUB>(L<SUB>2</SUB>V(0)) of the mod 3 Moore spectrum from π<SUB>*</SUB>(L<SUB>2</SUB>V(1)) by the Bockstein spectral sequence (BSS). Actually, we first compute the E<SUB>2</SUB>term of the ANSS by the BSS and then study the AdamsNovikov differentials, and obtain E<SUB>∞</SUB>=E<SUB>10</SUB> as well.
Journal

 Tokyo Sugaku Kaisya Zasshi

Tokyo Sugaku Kaisya Zasshi 52(1), 6590, 200001
The Mathematical Society of Japan