A modular description of the K(2)-local sphere at the prime 3

Mark Behrens

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A modular description of the K(2)-local sphere at the prime 3

Mark Behrens

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Abstract

Using degree N isogenies of elliptic curves, we produce a spectrum Q(N). This spectrum is built out of spectra related to tmf. At p=3 we show that the K(2)-local sphere is built out of Q(2) and its K(2)-local Spanier-Whitehead dual. This gives a conceptual reinterpretation a resolution of Goerss, Henn, Mahowald, and Rezk.

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Mark Behrens. 2005-08-16. A modular description of the K(2)-local sphere at the prime 3. https://arxiv.org/abs/math/0507184

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