The Rational Homotopy of the K(2)-Local Sphere and the Chromatic Splitting Conjecture for the Prime 3 and Level 2

We calculate the rational homotopy of the $K(2)$-local sphere $L_{K(2)}S^0$ at the prime 3 and confirm Hopkins' chromatic splitting conjecture for $p=3$ and $n=2$.

2010 Mathematics Subject Classification: 55P42

Keywords and Phrases: Chromatic stable homotopy theory

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