Spectroscopy of an extreme [OIII] emitting active galactic nucleus at
  $z=3.212$: implications for the reionisation era
  Reionisation-era galaxies often display intense nebular emission lines, both
in rest-frame optical ([OIII]+H$\beta$) and ultraviolet (UV; CIII], CIV). How
such strong nebular emission is powered remains unclear, with both active
galactic nuclei (AGN) and hot stars considered equally viable. The UV continuum
slopes of these early systems tend to be very blue ($\beta<-2$), reflecting
minimal dust obscuration, young ages, and low metallicities. This contrasts
with narrow-lined AGN at $z\sim2-3$, whose UV slopes are significantly redder
($\beta>-1$) than typical star-forming systems in the reionisation era. To
investigate the properties of AGN in the reionisation era, we have conducted a
search for potential examples of rare analogues with blue continua at
intermediate redshift ($z\sim2-3$). Our goals are to determine whether AGN with
intense line emission and blue continua exist and thereby to establish the
range of rest-frame UV and optical line ratios in this population. In this
paper we report the detection of a X-ray luminous AGN at $z=3.21$ (UDS-24561)
with extreme [OIII]+H$\beta$ line emission (EW $=1300$ \r{A}) and a blue UV
continuum slope ($\beta=-2.34$). MMT/Binospec and Keck/MOSFIRE spectra indicate
rest-frame UV line ratios consistent with AGN photoionisation models and
rest-frame optical lines with both a narrow component (FWHM $=154$ km$/$s) and
extended broad wings (FWHM $=977$ km$/$s), consistent with outflowing gas. We
describe how such objects can be identified in future JWST emission line
surveys in the reionisation era, thereby providing a valuable census of AGN
activity at $z>6$ and understanding their contribution to cosmic reionisation.
