  We investigate for the first time the effects of a Warm Dark Matter (WDM)
power spectrum on the statistical properties of galaxies using a semi-analytic
model of galaxy formation. The WDM spectrum we adopt as a reference case is
suppressed - compared to the standard Cold Dark Matter (CDM) case - below a
cut-off scale ~ 1 Mpc corresponding (for thermal relic WDM particles) to a mass
m_X=0.75 keV. This ensures consistency with present bounds provided by the
microwave background WMAP data and by the comparison of hydrodynamical N-body
simulations with observed Lyman-{\alpha} forest. We run our fiducial
semi-analytic model with such a WDM spectrum to derive galaxy luminosity
functions (in B, UV, and K bands) and the stellar mass distributions over a
wide range of cosmic epochs, to compare with recent observations and with the
results in the CDM case. The predicted color distribution of galaxies in the
WDM model is also checked against the data. When compared with the standard CDM
case, the luminosity and stellar mass distributions we obtain assuming a WDM
spectrum are characterized by: i) a flattening of the faint end slope and ii) a
sharpening of the cutoff at the bright end for z \lesssim 0.8. We discuss how
the former result is directly related to the smaller number of low-mass haloes
collapsing in the WDM scenario, while the latter is related to the smaller
number of satellite galaxies accumulating in massive haloes at low redshift,
thus suppressing the accretion of small lumps on the central, massive galaxies.
These results shows how a adopting a WDM power spectrum may contribute to solve
two major problems of CDM galaxy formation scenarios, namely, the excess of
predicted faint (low mass) galaxies at low and - most of all - high redshifts,
and the excess of bright (massive) galaxies at low redshifts.
