The ALMA view of the high-redshift relation between supermassive black
  holes and their host galaxies
  This work aims at studying the $M_{BH}-M_{dyn}$ relation of a sample of
$2<z<7$ quasars by constraining their host galaxy masses through full
kinematical modeling of the cold gas kinematics, thus avoiding all possible
biases and effects introduced by the rough virial estimates usually adopted so
far. For this purpose we retrieved public observations of $72$ quasar host
galaxies observed in ${\rm [CII]_{158\mu m}}$ or ${\rm CO}$ transitions with
the Atacama Large Millimeter Array (ALMA). We then selected those quasars whose
line emission is spatially resolved and performed a kinematic analysis on ALMA
observations. We estimated the dynamical mass of the systems by modeling the
gas kinematics with a rotating disc taking into account geometrical and
instrumental effects. Our dynamical mass estimates, combined with $M_{BH}$
obtained from literature and our own new ${\rm CIV}\lambda1550$ observations,
have allowed us to investigate the $ M_{BH}/M_{dyn}$ in the early Universe.
Overall we obtained a sample of $10$ quasars at $z\sim2-7$ in which line
emission is detected with high S/N ($> 5-10$) and the gas kinematics is
spatially resolved and dominated by ordered rotation. The estimated dynamical
masses place $6$ out of $10$ quasars above the local relation yielding to a
$M_{BH}/M_{dyn}$ ratios $\sim10\times$ higher than those estimated in low-$z$
galaxies. On the other hand, we found that $4$ quasars at $z\sim 4-6$ have
dynamical-to-BH mass ratios consistent with what is observed in early-type
galaxies in the local Universe.
