## Abstract

There is only one nontrivial localization of π_{*}S_{.p)} (the chromatic localization at v_{0} D p), but there are infinitely many nontrivial localizations of the Adams E_{2} page for the sphere. The first nonnilpotent element in the E_{2} page after v_{0} is b_{10} 2 Ext_{A}^{2,2p.p 1)}.F_{p}, F_{p} ). We work at p D 3 and study b_{10}^{1}Ext_{*}^{,}_{*P}.F_{3}, F_{3}) (where P is the algebra of dual reduced powers), which agrees with the infinite summand Ext_{P*}^{,}_{*}.F_{3}, F_{3}) of Ext_{A*}^{,}_{*}.F_{3}, F_{3}) above a line of slope_{23}^{1}. We compute up to the E_{9} page of an Adams spectral sequence in the category Stable.P ) converging to b_{10}^{1}Ext_{*}^{,}_{*P}.F_{3}, F_{3}), and conjecture that the spectral sequence collapses at E_{9}. We also give a complete calculation of b_{10}^{1}Ext_{*}^{,}_{*P}.F_{3}, F_{3}[E_{1}^{3}]).

Original language | English (US) |
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Pages (from-to) | 1965-2028 |

Number of pages | 64 |

Journal | Algebraic and Geometric Topology |

Volume | 20 |

Issue number | 4 |

DOIs | |

State | Published - 2020 |

## ASJC Scopus subject areas

- Geometry and Topology