Delta-discreteG–spectra and iterated homotopy fixed points

Abstract

Let G be a profinite group with finite virtual cohomological dimension and let X be a discrete G -spectrum. If H and K are closed subgroups of G , with H C K , then, in general, the K=H -spectrum X hH is not known to be a continuous K=H -spectrum, so that it is not known (in general) how to define the iterated homotopy fixed point spectrum .X hH / hK =H . To address this situation, we define homotopy fixed points for delta-discrete G -spectra and show that the setting of delta-discrete G -spectra gives a good framework within which to work. In particular, we show that by using delta-discrete K=H -spectra, there is always an iterated homotopy fixed point spectrum, denoted