## Abstract

We construct a spectral sequence converging to the homotopy set of maps from a spectrum to the K(n)-localization of the K (n + 1)-local sphere. We also construct a map of spectral sequences from the K(n)-local E_{n}-Adams spectral sequence to the preceding one. Then we compare the map on E_{2}-terms with a map induced by the inflation maps of continuous cohomology groups for Morava stabilizer groups. As an application we show that ζ_{n} in π_{-1}(L_{K(n)}S^{0}) represented by the reduced norm map in the K (n)-local E_{n}-Adams spectral sequence has a nontrivial image under the map π_{*} (L_{K(n)}S^{0}) → π_{*} (L_{K(n)}L_{K(n+1)}S^{0}).

Original language | English |
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Pages (from-to) | 439-471 |

Number of pages | 33 |

Journal | Pacific Journal of Mathematics |

Volume | 250 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2011 |

## Keywords

- Adams spectral sequence
- K(n)-localization
- Morava E-theory

## ASJC Scopus subject areas

- Mathematics(all)

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