  We present high resolution (0.3") Atacama Large Millimeter Array (ALMA) 870um
imaging of five z~1.5-4.5 X-ray detected AGN with luminosities of
L(2-8keV)>10^42 erg/s. These data provide a >~20x improvement in spatial
resolution over single-dish rest-frame FIR measurements. The sub-millimetre
emission is extended on scales of FWHM~0.2"-0.5", corresponding to physical
sizes of 1-3 kpc (median value of 1.8 kpc). These sizes are comparable to the
majority of z=1-5 sub-millimetre galaxies (SMGs) with equivalent ALMA
measurements. In combination with spectral energy distribution analyses, we
attribute this rest-frame far-infrared (FIR) emission to dust heated by star
formation. The implied star-formation rate surface densities are ~20-200
Mo/yr/kpc^2, which are consistent with SMGs of comparable FIR luminosities
(i.e., L(IR)~[1-5]x10^(12)Lo). Although limited by a small sample of AGN, which
all have high FIR luminosities, our study suggests that the kpc-scale spatial
distribution and surface density of star formation in high-redshift
star-forming galaxies is the same irrespective of the presence of X-ray
detected AGN.
