Vol. 250, No. 2, 2011

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

Takeshi Torii

Vol. 250 (2011), No. 2, 439–471
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 π1(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).

Keywords
Adams spectral sequence, K(n)-localization, Morava E-theory
Mathematical Subject Classification 2000
Primary: 55T25, 55P42
Secondary: 55Q51, 55N22, 55N20
Milestones
Received: 3 April 2009
Revised: 17 December 2009
Accepted: 4 February 2011
Published: 31 March 2011
Authors
Takeshi Torii
Department of Mathematics
Okayama University
Okayama 700-8530
Japan