ﻻ يوجد ملخص باللغة العربية
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}).
If K is a discrete group and Z is a K-spectrum, then the homotopy fixed point spectrum Z^{hK} is Map_*(EK_+, Z)^K, the fixed points of a familiar expression. Similarly, if G is a profinite group and X is a discrete G-spectrum, then X^{hG} is often gi
Following a suggestion of Hovey and Strickland, we study the category of $K(k) vee K(k+1) vee cdots vee K(n)$-local spectra. When $k = 0$, this is equivalent to the category of $E(n)$-local spectra, while for $k = n$, this is the category of $K(n)$-l
In this paper we use the approach introduced in an earlier paper by Goerss, Henn, Mahowald and Rezk in order to analyze the homotopy groups of L_{K(2)}V(0), the mod-3 Moore spectrum V(0) localized with respect to Morava K-theory K(2). These homotopy
We give a new description of Rosenthals generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.
We introduce a computationally tractable way to describe the $mathbb Z$-homotopy fixed points of a $C_{n}$-spectrum $E$, producing a genuine $C_{n}$ spectrum $E^{hnmathbb Z}$ whose fixed and homotopy fixed points agree and are the $mathbb Z$-homotopy