The Modulo Two Homotopy Groups of the 𝐿₂-Localization of the Ravenel Spectrum

Abstract

The Ravenel spectra T(m) for non-negative integers m interpolate between the sphere spectrum and the Brown-Peterson spectrum. Let L₂ denote the Bousfield-Ravenel localization functor with respect to v₂^−1 BP. In this paper, we determine the homotopy groups Ï€_∗(L₂T(m) : ℤ/2) = [M₂, L₂T(m)]_∗ for m > 1, where M₂ denotes the modulo two Moore spectrum.