### 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**K(n)-localization of the K(n+1)-local En+1-Adams spectral sequences.** / Torii, Takeshi.

Research output: Contribution to journal › Article

*Pacific Journal of Mathematics*, vol. 250, no. 2, pp. 439-471. https://doi.org/10.2140/pjm.2011.250.439

}

TY - JOUR

T1 - K(n)-localization of the K(n+1)-local En+1-Adams spectral sequences

AU - Torii, Takeshi

PY - 2011

Y1 - 2011

N2 - 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 En-Adams spectral sequence to the preceding one. Then we compare the map on E2-terms with a map induced by the inflation maps of continuous cohomology groups for Morava stabilizer groups. As an application we show that ζn in π-1(LK(n)S0) represented by the reduced norm map in the K (n)-local En-Adams spectral sequence has a nontrivial image under the map π* (LK(n)S0) → π* (LK(n)LK(n+1)S0).

AB - 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 En-Adams spectral sequence to the preceding one. Then we compare the map on E2-terms with a map induced by the inflation maps of continuous cohomology groups for Morava stabilizer groups. As an application we show that ζn in π-1(LK(n)S0) represented by the reduced norm map in the K (n)-local En-Adams spectral sequence has a nontrivial image under the map π* (LK(n)S0) → π* (LK(n)LK(n+1)S0).

KW - Adams spectral sequence

KW - K(n)-localization

KW - Morava E-theory

UR - http://www.scopus.com/inward/record.url?scp=79953681331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79953681331&partnerID=8YFLogxK

U2 - 10.2140/pjm.2011.250.439

DO - 10.2140/pjm.2011.250.439

M3 - Article

AN - SCOPUS:79953681331

VL - 250

SP - 439

EP - 471

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -