  The Fermi Gamma-ray Observatory discovered about a thousand extragalactic
sources emitting energy from 100 MeV to 100 GeV. The majority of these sources
belong to the class of blazars characterized by a quasi-featureless optical
spectrum (BL Lac Objects). This hampers the determination of their redshift and
therefore hinders the characterization of this class of objects. To investigate
the nature of these sources and to determine their redshift, we are carrying
out an extensive campaign using the 10m Gran Telescopio Canarias to obtain high
S/N ratio optical spectra. These observations allow us to confirm the blazar
nature of the targets, to find new redshifts or to set stringent limits on the
redshift based on the minimum equivalent width of specific absorption features
that can be measured in the spectrum and are expected from their host galaxy,
assuming it is a massive elliptical galaxy. These results are of importance for
the multi-frequencies emission models of the blazars, to test their extreme
physics, to shed light on their cosmic evolution and abundance in the far
Universe. These gamma emitters are also of great importance for the
characterization of the extragalactic background light through the absorption
by the IR-optical background photons.
