  We present predictions on the evolution of the Tully-Fisher (TF) relation
with redshift, based on cosmological N-body/hydrodynamical simulations of disc
galaxy formation and evolution. The simulations invoke star formation and
stellar feedback, chemical evolution with non-instantaneous recycling,
metallicity dependent radiative cooling and effects of a meta-galactic UV
field, including simplified radiative transfer.
  At z=0, the simulated and empirical TF relations are offset by about 0.4
magnitudes (1 sigma) in the B and I bands. The origin of these offsets is
somewhat unclear, but it may not necessarily be a problem of the simulations
only.
  As to evolution, we find a brightening of the TF relation between z=0 and z=1
of about 0.85 mag in rest-frame B band, with a non-evolving slope. The
brightening we predict is intermediate between the (still quite discrepant)
observational estimates.
  This evolution is primarily a luminosity effect, while the stellar mass TF
relation shows negligible evolution. The individual galaxies do gain stellar
mass between z=1 and z=0, by a 50-100%; but they also correspondingly increase
their characteristic circular speed. As a consequence, individually they mainly
evolve ALONG the stellar mass TF relation, while the relation as such does not
show any significant evolution.
