Redshift determination of the BL Lac object 3C66A by the detection of
  its host galaxy cluster at $z=0.340$
  The BL Lac object 3C66A is one of the most luminous extragalactic sources at
TeV $\gamma$-rays (VHE, i.e. $E >100$ GeV). Since TeV $\gamma$-ray radiation is
absorbed by the extragalactic background light (EBL), it is crucial to know the
redshift of the source in order to reconstruct its original spectral energy
distribution, as well as to constrain EBL models. However, the optical spectrum
of this BL\,Lac is almost featureless, so a direct measurement of $z$ is very
difficult; in fact, the published redshift value for this source ($z=0.444$)
has been strongly questioned. Based on EBL absorption arguments, several
constraints to its redshift, in the range $0.096 < z < 0.5$, were proposed.
  Since these AGNs are hosted, typically, in early type galaxies that are
members of groups or clusters, we have analysed spectro-photometrically the
environment of 3C66A, with the goal of finding the galaxy group hosting this
blazar. This study was made using optical images of a $5.5 \times
5.5$\,arcmin$^{2}$ field centred on the blazar, and spectra of 24 sources
obtained with Gemini/GMOS-N multi-object spectroscopy.
  We found spectroscopic evidence of two galaxy groups along the blazar's line
of sight: one at $z \simeq 0.020$ and a second one at $z \simeq 0.340$. The
first one is consistent with a known foreground structure, while the second
group here presented has six spectroscopically confirmed members. Their
location along a red sequence in the colour-magnitude diagram allows us to
identify 34 additional candidate members of the more distant group. The
blazar's spectrum shows broad absorption features that we identify as arising
in the intergalactic medium, thus allowing us to tentatively set a redshift
lower limit at $z_{3C66A} \ge 0.33$. As a consequence, we propose that 3C66A is
hosted in a galaxy that belongs to a cluster at $z=0.340$.
