  We explore the role of environment in the evolution of galaxies over
0.1<z<0.7 using the final zCOSMOS-bright data set. Using the red fraction of
galaxies as a proxy for the quenched population, we find that the fraction of
red galaxies increases with the environmental overdensity and with the stellar
mass, consistent with previous works. As at lower redshift, the red fraction
appears to be separable in mass and environment, suggesting the action of two
processes: mass and environmental quenching. The parameters describing these
appear to be essentially the same at z~0.7 as locally. We explore the relation
between red fraction, mass and environment also for the central and satellite
galaxies separately, paying close attention to the effects of impurities in the
central-satellite classification and using carefully constructed samples
matched in stellar mass. There is little evidence for a dependence of the red
fraction of centrals on overdensity. Satellites are consistently redder at all
overdensities, and the satellite quenching efficiency increases with
overdensity at 0.1<z<0.4. This is less marked at higher redshift, but both are
nevertheless consistent with the equivalent local measurements. At a given
stellar mass, the fraction of galaxies that are satellites also increases with
the overdensity. At a given overdensity and mass, the obtained relation between
the environmental quenching and the satellite fraction agrees well with the
satellite quenching efficiency, demonstrating that the environmental quenching
in the overall population is consistent with being entirely produced through
the satellite quenching process at least up to z=0.7. However, despite the
unprecedented size of our high redshift samples, the associated statistical
uncertainties are still significant and our statements should be understood as
approximations to physical reality, rather than physically exact formulae.
