ALMA Observations of the Sub-kpc Structure of the Host Galaxy of a z=
  6.5 Lensed Quasar: A Rotationally-Supported Hyper-Starburst System at the
  Epoch of Reionization
  We report ALMA observations of the dust continuum and {\cii} emission of the
host galaxy of J0439+1634, a gravitationally lensed quasar at $z=6.5$.
Gravitational lensing boosts the source-plane resolution to $\sim0\farcs15$
$(\sim0.8\text{ kpc})$. The lensing model derived from the ALMA data is
consistent with the fiducial model in \citet{fan19} based on {\it HST} imaging.
The host galaxy of J0439+1634 can be well-fitted by a S\'ersic profile
consistent with an exponential disk, both in the far-infrared (FIR) continuum
and the {\cii} emission. The overall magnification is $4.53\pm0.05$ for the
continuum and $3.44\pm0.05$ for the {\cii} line. The host galaxy of J0439+1634
is a compact ultra-luminous infrared galaxy, with a total star formation rate
(SFR) of $1.56\times10^{3}M_\odot/\text{year}$ after correcting for lensing and
an effective radius of $0.74$ kpc. The resolved regions in J0439+1634 follow
the ``{\cii} deficit," where the {\cii}-to-FIR ratio decreases with FIR surface
brightness. The reconstructed velocity field of J0439+1634 appears to be
rotation-like. The maximum line-of-sight rotation velocity of 130 km/s at a
radius of 2 kpc. However, our data cannot be fit by an axisymmetric thin
rotating disk, and the inclination of the rotation axis, $i$, remains
unconstrained. We estimate the dynamical mass of the host galaxy to be
$7.9\sin^{-2}(i)\times10^{9}M_\odot$. J0439+1634 is likely to have a high
gas-mass fraction and an oversized SMBH compared to local relations. The SFR of
J0439+1634 reaches the maximum possible values, and the SFR surface density is
close to the highest value seen in any star-forming galaxy currently known in
the universe.
