Abstract
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).
| Original language | English |
|---|---|
| Pages (from-to) | 1097-1103 |
| Number of pages | 7 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 140 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2012 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Every K(n)-local spectrum is the homotopy fixed points of its Morava module. / Davis, Daniel G.; Torii, Takeshi.
In: Proceedings of the American Mathematical Society, Vol. 140, No. 3, 2012, p. 1097-1103.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Every K(n)-local spectrum is the homotopy fixed points of its Morava module
AU - Davis, Daniel G.
AU - Torii, Takeshi
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).
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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 -