The homotopy groups of SE(2) at p⩾5 revisited

We present a new technique for analyzing the v0-Bockstein spectral sequence studied by Shimomura and Yabe. Employing this technique, we derive a conceptually simpler presentation of the homotopy groups of the E(2)-local sphere at primes p⩾5. We identify and correct some errors in the original Shimomura–Yabe calculation. We deduce the related K(2)-local homotopy groups, and discuss their manifestation of Gross–Hopkins duality.