Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A modular description of the K(2)-local sphere at the prime 3   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.

36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin