  We use many-body perturbation theory, the state-of-the-art method for band
gap calculations, to compute the band offsets at the Si/SiO$_2$ interface. We
examine the adequacy of the usual approximations in this context. We show that
(i) the separate treatment of band-structure and potential lineup
contributions, the latter being evaluated within density-functional theory, is
justified, (ii) most plasmon-pole models lead to inaccuracies in the absolute
quasiparticle corrections, (iii) vertex corrections can be neglected, (iv)
eigenenergy self-consistency is adequate. Our theoretical offsets agree with
the experimental ones within 0.3 eV.
