  The constraints on neutrino masses led to the revision of their cosmological
role, since the existence of a cosmological neutrino background is a clear
prediction of the standard cosmological model. In this paper, we study the
impact of such background on the spatial distribution of both Dark Matter (DM)
and galaxies, by coupling $N$-body numerical simulations with semi-analytic
models (SAMs) of galaxy formation. Cosmological simulations including massive
neutrinos predict a slower evolution of DM perturbations with respect to the
$\Lambda$CDM runs with the same initial conditions and a suppression on the
matter power spectrum on small and intermediate scales, thus impacting on the
predicted properties of galaxy populations. We explicitly show that most of
these deviations are driven by the different $\sigma_8$ predicted for
cosmologies including a massive neutrino background. We conclude that
independent estimates of $\sigma_8$ are needed, in order to unambiguously
characterise the effect of this background on the growth of structures. Galaxy
properties alone are a weak tracer of deviations with respect to the
$\Lambda$CDM run, but their combination with the overall matter distribution at
all scales allows to disentangle between different cosmological models.
Moreover, these deviations go on opposite direction with respect to competing
models like modified gravity, thus weakening any detectable cosmological
signal. Given the ubiquitous presence of a neutrino background, these effects
have to be taken into account in future missions aimed at constraining the
properties of the "Dark" components of the Universe.
