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arXiv · 1610.00158

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

Irina Bobkova·Paul G. Goerss
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Abstract

We provide a topological duality resolution for the spectrum $E_2^{h\mathbb{S}_2^1}$, which itself can be used to build the $K(2)$-local sphere. The resolution is built from spectra of the form $E_2^{hF}$ where $E_2$ 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 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.

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Irina Bobkova, Paul G. Goerss. 2016-10-01. Topological resolutions in K(2)-local homotopy theory at the prime 2. https://doi.org/10.1112/topo.12076

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