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

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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 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).

Original languageEnglish
Pages (from-to)439-471
Number of pages33
JournalPacific Journal of Mathematics
Volume250
Issue number2
DOIs
Publication statusPublished - Apr 11 2011

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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