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January, 2000 The homotopy groups of the L2-localized mod 3 Moore spectrum
J. Math. Soc. Japan 52(1): 65-90 (January, 2000). DOI: 10.2969/jmsj/05210065


At each prime number p, the homotopy groups π*(L2S0) of the v21BP-localized sphere spectrum play an crucial role to understand the category of v21BP-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.


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Katsumi SHIMOMURA. "The homotopy groups of the L2-localized mod 3 Moore spectrum." J. Math. Soc. Japan 52 (1) 65 - 90, January, 2000.


Published: January, 2000
First available in Project Euclid: 10 June 2008

zbMATH: 0946.55006
MathSciNet: MR1727130
Digital Object Identifier: 10.2969/jmsj/05210065

Primary: 55Q45
Secondary: 55P42 , 55Q52 , 55T15

Keywords: Adams-Novikov spectral sequence , Bousfield-Ravenel localization , Homotopy groups

Rights: Copyright © 2000 Mathematical Society of Japan

Vol.52 • No. 1 • January, 2000
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