  We present a study of optically-selected Type II AGN at 0.5 < z < 0.9 from
the VIPERS and VVDS surveys, to investigate the connection between AGN activity
and physical properties of their host galaxies. The host stellar mass is
estimated through spectral energy distribution fitting with the CIGALE code,
and star formation rates are derived from the [OII]$\lambda$3727 $\r{A}$ line
luminosity. We find that 49% of the AGN host galaxies are on or above the main
sequence (MS), 40% lie in the sub-MS locus, and 11% in the quiescent locus.
Using the [OIII]$\lambda$5007 $\r{A}$ line luminosity as a proxy of the AGN
power, we find that at fixed AGN power Type II AGN host galaxies show a bimodal
behaviour: systems with host galaxy stellar mass <10$^{10}$ M$_{\odot}$, reside
along the MS or in the starbursts locus (high-SF Type II AGN), while systems
residing in massive host-galaxies (>10$^{10}$ M$_{\odot}$) show a lower level
of star formation (low-SF Type II AGN). At all stellar masses, the offset from
the MS is positively correlated with the AGN power. We interpret this
correlation as evidence of co-evolution between the AGN and the host, possibly
due to the availability of cold gas. In the most powerful AGN with host
galaxies below the MS we find a hint, though weak, of asymmetry in the [OIII]
line profile, likely due to outflowing gas, consistent with a scenario in which
AGN feedback removes the available gas and halts the star formation in the most
massive hosts.
