English

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

Algebraic Topology 2007-05-23 v2

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.

Cite

@article{arxiv.math/0507184,
  title  = {A modular description of the K(2)-local sphere at the prime 3},
  author = {Mark Behrens},
  journal= {arXiv preprint arXiv:math/0507184},
  year   = {2007}
}

Comments

72 pages, 1 figure, to appear in Topology. Typos in Diagrams (2.11.2) and (2.11.3) fixed, and 2 lemmas added in Section 2.11 to prove that Diagram (2.11.4) exists