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We analyse the stellar populations in the host galaxies of 53 X-ray selectedoptically dull active galactic nuclei (AGN) at 0.34<z<1.07 with ultra-deep(m=26.5) optical medium-band (R~50) photometry from the Survey for High-zAbsorption Red and Dead Sources (SHARDS). The spectral resolution of SHARDSallows us to consistently measure the strength of the 4000 AA break, Dn(4000),a reliable age indicator for stellar populations. We confirm that most X-rayselected moderate-luminosity AGN (L_X<10^44 erg/s) are hosted by massivegalaxies (typically M*>10^10.5 M_sun) and that the observed fraction ofgalaxies hosting an AGN increases with the stellar mass. A careful selection ofrandom control samples of inactive galaxies allows us to remove the stellarmass and redshift dependencies of the AGN fraction to explore trends withseveral stellar age indicators. We find no significant differences in thedistribution of the rest-frame U-V colour for AGN hosts and inactive galaxies,in agreement with previous results. However, we find significantly shallower4000 AA breaks in AGN hosts, indicative of younger stellar populations. Withthe help of a model-independent determination of the extinction, we obtainextinction-corrected U-V colours and light-weighted average stellar ages. Wefind that AGN hosts have younger stellar populations and higher extinctioncompared to inactive galaxies with the same stellar mass and at the sameredshift. We find a highly significant excess of AGN hosts with Dn(4000)~1.4and light weighted average stellar ages of 300-500 Myr, as well as a deficit ofAGN in intrinsic red galaxies. We interpret failure in recognising these trendsin previous studies as a consequence of the balancing effect in observedcolours of the age-extinction degeneracy.

Higher prevalence of X-ray selected AGN in intermediate age galaxies up to z~1