Every K(n)-local spectrum is the homotopy fixed points of its Morava module
Daniel G. Davis,Takeshi Torii +1 more
- Vol. 140, Iss: 3, pp 1097-1103
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TLDR
In this paper, it was shown that for any S-cofibrant spectrum X, the strongly convergent Adams-type spectral sequence is isomorphic to the descent spectral sequence that abuts to (L.K(n)(E_n \wedge X))^{hG_n} for any (S-coffibrant) spectrum X.Abstract:
Let n \geq 1 and let p be any prime. Also, let E_n be the Lubin-Tate spectrum, G_n 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 note, show that if X is a finite spectrum, then the localization L_{K(n)}(X) is equivalent to the homotopy fixed point spectrum (L_{K(n)}(E_n \wedge X))^{hG_n}, which is formed with respect to the continuous action of G_n on L_{K(n)}(E_n \wedge X). In this note, 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 \pi_\ast(L_{K(n)}(X)) is isomorphic to the descent spectral sequence that abuts to \pi_\ast((L_{K(n)}(E_n \wedge X))^{hG_n}).read more
Citations
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Strictly commutative realizations of diagrams over the Steenrod algebra and topological modular forms at the prime 2
Tyler Lawson,Niko Naumann +1 more
TL;DR: In this article, a generalized truncated Brown-Peterson spectrum of chromatic height 2 at the prime 2 was constructed as an E∞-ring spectrum, based on the study of elliptic curves with level-3 structure.
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Constructing the determinant sphere using a Tate twist
TL;DR: In this article, the Tate sphere was constructed, which is a complete sphere with a continuous action of $k(n)p^\times, where n is the number of points in the Tate spectrum.
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A descent spectral sequence for arbitrary K(n)-local spectra with explicit e 2-term
Daniel G. Davis,Tyler Lawson +1 more
TL;DR: In this paper, a descent spectral sequence with abutment π∗(LK(n)(X)) and E2-term equal to the continuous cohomology of the extended Morava stabilizer group was constructed.
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Discrete G -spectra and embeddings of module spectra
TL;DR: In this paper, the authors consider an embedding of module objects in spectra into a category of modules in discrete G-spectra, and study the relationship between the embedding and the homotopy fixed points functor.
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Constructing the determinant sphere using a Tate twist
TL;DR: In this article, the Tate sphere S(1) is constructed, which is a p-complete sphere with a natural continuous action of $$\mathbb {Z}_p^\times $$¯¯¯¯.
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