TY - JOUR
T1 - Every K(n)-local spectrum is the homotopy fixed points of its Morava module
AU - Davis, Daniel G.
AU - Torii, Takeshi
N1 - Copyright:
Copyright 2011 Elsevier B.V., All rights reserved.
PY - 2012
Y1 - 2012
N2 - Let n ≥ 1 and let p be any prime. Also, let En be the Lubin-Tate spectrum, Gn the extended Morava stabilizer group, and K(n) the nth Morava K-theory spectrum. Then work of Devinatz and Hopkins and some results due to Behrens and the first author of this paper show that if X is a finite spectrum, then the localization LK(n)(X) is equivalent to the homotopy fixed point spectrum (LK(n)(En ∧ X))hGn, which is formed with respect to the continuous action of Gn on LK(n)(En ∧ X). In this paper, we show that this equivalence holds for any (S-cofibrant) spectrum X. Also, we show that for all such X, the strongly convergent Adams-type spectral sequence abutting to π*(LK(n)(X)) is isomorphic to the descent spectral sequence that abuts to π*((LK(n)(En ∧ X))hGn).
AB - Let n ≥ 1 and let p be any prime. Also, let En be the Lubin-Tate spectrum, Gn the extended Morava stabilizer group, and K(n) the nth Morava K-theory spectrum. Then work of Devinatz and Hopkins and some results due to Behrens and the first author of this paper show that if X is a finite spectrum, then the localization LK(n)(X) is equivalent to the homotopy fixed point spectrum (LK(n)(En ∧ X))hGn, which is formed with respect to the continuous action of Gn on LK(n)(En ∧ X). In this paper, we show that this equivalence holds for any (S-cofibrant) spectrum X. Also, we show that for all such X, the strongly convergent Adams-type spectral sequence abutting to π*(LK(n)(X)) is isomorphic to the descent spectral sequence that abuts to π*((LK(n)(En ∧ X))hGn).
UR - http://www.scopus.com/inward/record.url?scp=82255191455&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=82255191455&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-2011-11189-4
DO - 10.1090/S0002-9939-2011-11189-4
M3 - Article
AN - SCOPUS:82255191455
VL - 140
SP - 1097
EP - 1103
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 3
ER -