The homotopy groups of the E(2) local sphere at p > 3 revisited

TL;DR

This paper introduces a new method to analyze the homotopy groups of the E(2)-local sphere at primes greater than 3, simplifying previous calculations and correcting earlier errors, with implications for K(2)-local groups and duality.

Contribution

A novel technique for analyzing the v_0-Bockstein spectral sequence that simplifies and corrects prior computations of homotopy groups at p > 3.

Findings

Simplified presentation of E(2)-local sphere homotopy groups

Correction of errors in previous Shimomura-Yabe calculations

Insights into K(2)-local homotopy groups and Gross-Hopkins duality

Abstract

We present a new technique for analyzing the v_0-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 for p > 3. 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.