The goal of this paper is to develop some of the machinery necessary for doing
–local
computations in the stable homotopy category using duality resolutions at the prime
. The Morava stabilizer
group
admits a surjective
homomorphism to
whose
kernel we denote by
.
The algebraic duality resolution is a finite resolution of the trivial
–module
by modules induced from representations of finite subgroups of
. Its construction
is due to Goerss, Henn, Mahowald and Rezk. It is an analogue of their finite resolution of the
trivial
–module
at the
prime
.
The construction was never published and it is the main result in this paper. In the
process, we give a detailed description of the structure of Morava stabilizer group
at the
prime
.
We also describe the maps in the algebraic duality resolution with the precision
necessary for explicit computations.
Keywords
finite resolution, K(2)-local, chromatic homotopy theory
