The influence of rotation on turbulent convection is investigated with direct numerical simulation. The classical Rayleigh-Benard con guration is augmented with steady rotation about the vertical axis. Correspondingly, characterisation of the dynamics requires both the dimensionless Rayleigh number $Ra$ and the Taylor number $Ta$. With increasing $Ta$ the root-mean-square (rms) velocity variations are found to decrease, while the rms temperature variations increase. Under rotation a mean vertical temperature gradient develops in the bulk. Compared to the non-rotating case, at constant $Ra = 2.5\,10^6$ the Nusselt number increases up to approximately 5% at relatively low rotation rates, $Ta < Ta_m \approx 10^6$, and decreases strongly when $Ta$ is further increased. A striking change in the boundary layer structure arises when $Ta$ traverses an interval about $Ta_m$, as is expressed by the near-wall vertical-velocity skewness.