  We use a recently developed self-consistent $GW$ approximation to present
systematic \emph{ab initio} calculations of the conduction band spin splitting
in III-V and II-V zincblende semiconductors. The spin orbit interaction is
taken into account as a perturbation to the scalar relativistic hamiltonian.
These are the first calculations of conduction band spin splittings based on a
quasiparticle approach; and because the self-consistent $GW$ scheme accurately
reproduces the relevant band parameters, it is expected to be a reliable
predictor of spin splittings. The results are compared to the few available
experimental data and a previous calculation based on a model one-particle
potential. We also briefly address the widely used {\bf k}$\cdot${\bf p}
parameterization in the context of these results.
