The Algebraic Duality Resolution at p=2

الأصل · EN

The goal of this paper is to develop some of the machinery necessary for doing K(2)-local computations in the stable homotopy category using duality resolutions at the prime p=2. The Morava stabilizer group S₂ admits a norm whose kernel we denote by S₂¹. The algebraic duality resolution is a finite resolution of the trivial Z₂[[S₂¹]]-module Z₂ by modules induced from representations of finite subgroups of S₂¹. Its construction is due to Goerss, Henn, Mahowald and Rezk. It is an analogue of their finite resolution of the trivial Z₃[[G₂¹]]-module Z₃ at the prime p=3. 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 S₂ at the prime 2. We also describe the maps in the algebraic duality resolution with the precision necessary for explicit computations.