Homotopy fixed points for \(L_{K(n)}(E_{n}\land X)\) using the continuous action (Q2497509)

In this paper, it is shown that, if \(G\) is a closed subgroup of the profinite group of ring spectrum automorphisms of the Lubin-Tate spectrum (in the stable homotopy category), then \(E^\vee(X)\) is a continuous \(G\)-spectrum with homotopy fixed point spectrum \((E^\vee (X))^{hG}\), where \(E^\vee(X)=L_{K(n)}(E_n \wedge X)\) and \(K(n)\) is the \(n\)th Morava K-theory spectrum. A descent spectral sequence is also constructed with abutment \(\pi_*((E^\vee (X))^{hG})\).