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

By Mark Behrens. 2005

95 citations recorded by the source corpus.

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. AMS classic ation: Primary 55Q40, 55Q51, 55N34. Secondary 55S05, 14H52.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca522b256640d5adf17eeac3ec4c17a5e5705c7b

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In Geometry and Topology

1. Lennart Meier
2. M. Hill
3. Paul G. Goerss
4. I. Bobkova
5. A. Mathew
6. Kathryn Hess
7. Andrew Justin Blumberg
8. S. Schwede

In Mathematical Physics

1. Lennart Meier
2. I. Bobkova
3. Paul G. Goerss
4. M. Hill
5. A. Mathew
6. John E. Harper
7. Kathryn Hess
8. S. Schwede

Citations in the corpus

• Topological resolutions in K(2) ‐local homotopy theory at the prime 2 (2016, background): “ality group of dimension 3, this is called a duality resolution. This resolution and related resolutions were instrumental in exploring the K(2)-local category at primes p>2. See [GHM04], [HKM13], [Beh06], [GHM14], [GHMR15], TOPOLOGICAL RESOLUTIONS IN K(2)-LOCAL HOMOTOPY THEORY 3 [GH16], and [Lad”
• The C2–spectrum Tmf1(3) and its invertible modules (2015, methodology): “First, we mention the Q(l)-spectra defined by Behrens ([Beh06], [BO12]), which are built from TMF with level structures and provide approximations of the K(2)-local sphere.”