Title: An application of continuous homotopy fixed points to chromatic homotopy theory
Speaker: Daniel Davis (University of Louisiana)
Abstract: Let $S^g$ be the "less algebraic" object in the Goerss-Hopkins Linearization Conjecture for the extended Morava stabilizer group $G_n$. Also, let $S^{-g}$ be the spectrum closely related to $S^g$ that is the dualizing spectrum for the Lubin-Tate spectrum. There are different presentations of these constructions (none published), and in the case of both $S^g$ and $S^{-g}$ there is a presentation that involves the continuous homotopy fixed points of a spectrum with respect to the trivial action of a profinite group. We give a hypothesis that when satisfied, shows that such homotopy fixed points can be built from the classifying space of the profinite group, so that the topology of the profinite group plays no role in the construction of the continuous homotopy fixed points. We give an example of when this hypothesis is satisfied.
