Topological resolutions in K(2)-local homotopy theory at the prime 2

We provide a topological duality resolution for the spectrum E₂ ^hs1/2, which itself can be used to build the K(2)-local sphere. The resolution is built from spectra of the form E₂ ^hF where E₂ is the Morava spectrum for the formal group of a supersingular curve at the prime 2 and F is a finite subgroup of the automorphisms of that formal group. The results are in complete analogy with the resolutions of Goerss, Henn, Mahowald and Rezk (Ann. of Math. (2) 162 (2005) 777–822) at the prime 3, but the methods are of necessity very different. As in the prime 3 case, the main difficulty is in identifying the top fiber; to do this, we make calculations using Henn's centralizer resolution.