  Intrinsic galaxy shape and angular momentum alignments can arise in
cosmological large-scale structure due to tidal interactions or galaxy
formation processes. Cosmological hydrodynamical simulations have recently come
of age as a tool to study these alignments and their contamination to weak
gravitational lensing. We probe the redshift and luminosity evolution of
intrinsic alignments in Horizon-AGN between z=0 and z=3 for galaxies with an
r-band absolute magnitude of <-20. Alignments transition from being radial at
low redshifts and high luminosities, dominated by the contribution of
ellipticals, to being tangential at high redshift and low luminosities, where
discs dominate the signal. This cannot be explained by the evolution of the
fraction of ellipticals and discs alone: intrinsic evolution in the amplitude
of alignments is necessary. The alignment amplitude of elliptical galaxies
alone is smaller in amplitude by a factor of ~2, but has similar luminosity and
redshift evolution as in current observations and in the nonlinear tidal
alignment model at projected separations of > 1 Mpc. Alignments of discs are
null in projection and consistent with current low redshift observations. The
combination of the two populations yields an overall amplitude a factor of ~4
lower than observed alignments of luminous red galaxies with a steeper
luminosity dependence. The restriction on accurate galaxy shapes implies that
the galaxy population in the simulation is complete only to an r-band absolute
magnitude of <-20. Higher resolution simulations will be necessary to avoid
extrapolation of the intrinsic alignment predictions to the range of
luminosities probed by future surveys.
