  We discuss a simple theory for neutrino masses where the total lepton number
is a local gauge symmetry spontaneously broken below the multi-TeV scale. In
this context, the neutrino masses are generated through the canonical seesaw
mechanism and a Majorana dark matter candidate is predicted from anomaly
cancellation. We discuss in great detail the dark matter annihilation channels
and find out the upper bound on the symmetry breaking scale using the
cosmological bounds on the relic density. Since in this context the dark matter
candidate has suppressed couplings to the Standard Model quarks, one can
satisfy the direct detection bounds even if the dark matter mass is close to
the electroweak scale. This theory predicts a light pseudo-Nambu-Goldstone
boson (the Majoron) associated to the mechanism of neutrino mass. We discuss
briefly the properties of the Majoron and the impact of the Big Bang
Nucleosynthesis bounds.
