The homotopy groups of 𝐿₂𝑇(1)/(𝑣₁) at an odd prime

In this paper, all spectra are localized at an odd prime. Let T ( 1 ) T(1) be the Ravenel spectrum characterized by B P ∗ BP_{\ast } -homology as B P ∗ [ t 1 ] BP_{\ast }[t_1] , T ( 1 ) / ( v 1 ) T(1)/(v_1) be the cofiber of the self-map v 1 : Σ 2 p − 2 T ( 1 ) → T ( 1 ) v_1: \Sigma ^{2p-2}T(1)\rightarrow T(1) and L 2 L_2 denote the Bousfield localization functor with respect to v 2 − 1 B P ∗ v_2^{-1}BP_{\ast } . In this paper, we determine the homotopy groups of L 2 T ( 1 ) / ( v 1 ) L_2T(1)/(v_1) .