The derived category of complex periodic K-theory localized at an odd prime

We prove that for an odd prime p, the derived category D(KU(p)) of the p-local complex periodic K-theory spectrum KU(p) is triangulated equivalent to the derived category of its homotopy ring π⁎KU(p). This implies that if p is an odd prime, the triangulated category D(KU(p)) is algebraic.