The $E(1)$-local Picard graded homotopy groups of the sphere spectrum at the prime two

Abstract

A bstract . Let E ð 1 Þ be the first Johnson-Wilson spectrum at the prime two. In this paper, we calculate the homotopy groups of the E ð 1 Þ -localized sphere spectrum with a grading over the Picard group of the stable homotopy category of E ð 1 Þ -local spectra.