Homotopy fixed points for L_K(n)(E_n ^ X) using the continuous action, by Daniel G. Davis

Note: This paper is to appear in the "Journal of Pure and Applied Algebra."

We use work due to Jardine and Thomason to obtain results in chromatic stable homotopy theory. The paper proceeds by developing the notion of a discrete G-spectrum, where G is a profinite group. For example, the K-theory spectrum of the separable closure k^sep of a field k is a discrete G-spectrum, where G is the Galois group of k^sep over k.

Abstract: Let G be a closed subgroup of G_n, the extended Morava stabilizer group. Let E_n be the Lubin-Tate spectrum, let X be an arbitrary spectrum with trivial G-action, and define E^(X) to be L_K(n)(E_n ^ X). We prove that E^(X) is a continuous G-spectrum with a G-homotopy fixed point spectrum, defined with respect to the continuous action. Also, we construct a descent spectral sequence whose abutment is the homotopy groups of the G-homotopy fixed point spectrum of E^(X). We show that the homotopy fixed points of E^(X) come from the K(n)-localization of the homotopy fixed points of the spectrum (F_n ^ X).

Daniel G. Davis <dgdavis@math.purdue.edu>