Brown-Comenetz duality and the Adams spectral sequence

We show that the class of p-complete connective spectra with finitely prese nted cohomology over the Steenrod algebra admits a duality theory related t o Brown-Comenetz duality. This construction also produces a full-plane vers ion of the classical Adams spectral sequence for such spectra, which conver ges to the homotopy groups of a "finite" localization.