The homotopy groups of the L_2-localized mod 3 Moore spectrum

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概要

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• 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>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, \ 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 Toda-Smith 4-cells 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 Adams-Novikov differentials, and obtain E<SUB>∞</SUB>=E<SUB>10</SUB> as well.

• 社団法人 日本数学会の論文
• 2000-01-00

著者

• Katsumi Shimomura

  Department Of Mathematics Faculty Of Science Kochi University

• Shimomura Katsumi

  Department Of Mathematics Faculty Of Education Tottori University

関連論文

• ${\rm BP}$-Hopf Module Spectrum and ${\rm BP}\sb *$-Adams Spectral Sequence : Dedicated to Professor Masahiro Sugawara on his 60th birthday
• The homotopy groups of an L2-localized type one finite spectrum at the prime 2
• On the action of $\beta_1$ in the stable homotopy of spheres at the prime 3
• The homotopy groups of the L_2-localized mod 3 Moore spectrum
• Existence of the Greek Letter Elements in the Stable Homotopy Groups of $E(n)_*$-Localized Spheres

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